Abstracts

Thursday, August 9, 2018 Session 1A: Plenary Session I Time: 8:45 am – 10:00 am Location: McKellar Room Chair: Xiaoming Liu, Western University 8:45 AM - 8:50 AM Announcements and introduction of Dean of Science, by Bruce Jones, Western University 8:50 AM – 9:00 AM Welcome to Western, by Matt Davison, Dean of Science, Western University

9:00 AM - 10:00 AM Keynote Presentation Title: Data analytics for insurance pricing Presenter: Katrien Antonio, KU Leuven (Belgium) and the University of Amsterdam (the Netherlands) Abstract: Insurance companies use predictive models for a variety of analytic tasks including pricing. In practice, these predictive models often use a selection of continuous, ordinal, nominal and spatial variables to differentiate risks. Such models should not only be competitive, but also interpretable by stakeholders (including the policyholder and the regulator), and easy to implement and to maintain in a production environment. Therefore, current actuarial literature puts focus on generalized linear models where ad hoc techniques or professional expertise are applied to remove variables and to group the levels within a variable. In this talk I will present an overview of recent work on the use of statistical learning methods for insurance pricing. I will discuss regularized (or: penalized) regression to obtain an automatic data-driven method for variable selection and variable binning in predictive modeling and shed light on the use of tree-based methods for insurance pricing.

Thursday, August 9, 2018 Session 2A: Actuarial Education I Time: 10:30 am – 12:00 pm Location: McKellar Room Chair: Jeff Beckley, Purdue University 10:30 AM - 11:00 AM Title: Specific Guidelines for Creating Two-Dimensional Syllabi with Challenging but not Overly- Difficult Problems Presenter: Russell Hendel, Towson University Abstract: OVERVIEW: Based on the psychology of executive function, specific techniques are presented for providing courses, possessing fixed syllabi, with problems that are both challenging but not overly difficult. Attendees completing the presentation will have a simple test by which to differentiate problems, facilitating selection of challenging but not overly difficult problems. TRADITIONAL APPROACH: A two-dimensional syllabus is a syllabus with two dimensions: i) the content dimension and ii) the problem dimension. Clearly, in teaching a preliminary exam course, it benefits the students if the illustrative problems selected, for lecture and homework, reflect challenges similar to the preliminary- exam problems. However, the “obvious” way to implement this goal is pedagogically unsound: The "obvious" way by which problems achieve exam-grade difficulty is by adding enough “pitfalls” to a core problem. For example, typical theory of interest problems (FM exam) can be raised to exam-level difficulty if their solution requires simultaneous consideration of typical FM pitfalls such as i) immediate-due , ii) interest rate conversions, iii) deferrals, iv) conversion of absolute dates to relative dates on a timeline, etc. However, it would be poor technique to base initial lectures and homework on such problems since they are overly difficult, throwing too much at the student. EXECUTIVE-FUNCTION PSYCHOLOGY: Executive function refers to the capacity of the mind to solve a problem using multiple modalities or areas. The calculus “rule of four” lists four modalities that good calculus problem and instruction should have: i) algebraic, ii) geometric, iii) computational and iv) verbal. In FM the “rule of four” corresponds to i) algebraic, ii) timelines, iii) time-value calculator lines and iv) verbal. Experiments show that using just two modalities is sufficient to create challenge. Challenge exists even for “vanilla” problems without further “pitfalls”. Examples are presented from all preliminary exam courses. 11:00 AM - 11:30 AM Title: Professionalism in Actuarial Science: Teaching Our Students to Be Actuaries, Not Just Test- Takers Presenter: Alisa Walch, University of Texas at Austin Abstract: While passing actuarial exams is essential for our students to land a full-time job, there's a lot more to being an actuary. It's important that we prepare them to be successful in their actuarial career and not just in the exam room. These are some ideas of how to incorporate professionalism into existing actuarial courses. 11:30 AM - 12:00 PM Title: Getting Students to Think Like Actuaries: Incorporating Professional Skills in the Classroom Presenter: Diana Skrzydlo, University of Waterloo Abstract: Inspired by a discussion at a previous SOA conference, I set out to incorporate more professional skills that actuaries need into the early actuarial science curriculum. In the first Life Contingencies course (a second year course), I introduced a segment called “Think Like an Actuary” to my tutorials, assignments, classes, and tests. I had students think critically about and debate ethical/professional issues such as genetic testing, predict the impact on the insurance

industry of external forces such as self-driving cars, write reports for various audiences, justify their assumptions, and make recommendations to hypothetical clients. I was incredibly impressed with the quality and depth of thought these young students were capable of, once they were actually asked to think about these issues. Many students reported that they found the activities beneficial for their future careers, made them see the discipline in a new light, and helped them realize that being an actuary was the right choice for them. In this session I will discuss the activities I used and how I integrated them into my course without losing any core material. I will give suggestions for incorporating similar activities into any actuarial course, at any level. I believe there is always room to help students develop the skills they will need to become confident, qualified members of the actuarial profession.

Thursday, August 9, 2018 Session 2B: Pensions and Retirement I Time: 10:30 am – 12:00 pm Location: UCC 146 Chair: Bruce Jones, Western University 10:30 AM - 11:00 AM Title: AHP application to Post- Retirement Planning and Decision Presenter: Marie-Claire Koissi, Actuarial Science Program, University of Wisconsin-Eau Claire Abstract: The Analytic Hierarchy Process (AHP) is a methodology based on pair- wise comparisonsthat relies on judgment to derive priority scales. An area of possible application of the AHP is retirement, where the AHP can be used for efficient asset allocation in order to meet retirees’ goals.In this talk, we will present an example of financial planning and discuss how the AHP can be used to accommodate a retiree’s set of goals. Keywords: AHP, Multicriteria decision, Retirement.

11:00 AM - 11:30 AM Title: A review of the proposed University Pension Plan for Ontario Presenter: Mary Hardy, University of Waterloo Abstract: The University Pension Plan Ontario (UPP) project promises a new multi-employer Defined Benefit pension plan for Ontario Universities. The benefits are generous, the brochures are attractive. The first three participants are expected to be Queen's University, University of Toronto and University of Guelph, with several other universities expressing an interest. In principle, current employees of these universities must agree to proceed through some kind of voting process, but it is hard to see how members will make an informed decision with the information available. In this talk I will review the risks and potential rewards of the proposed scheme, with numerical illustrations using a model pension plan to consider the impact of the funding, design and risk management decisions. 11:30 AM - 12:00 PM Title: Retirement planning with ambiguous investment and mortality risks Presenter: Yang Shen, York University Abstract: We study the strategic retirement planning problem for a wage earner facing stochastic lifetime. The wage earner aims to decide on the optimal portfolio choice, consumption and insurance buying rules over the pre-retirement phase, but meanwhile she concerns about the financial and mortality model uncertainty. In order to address the concern, the wage earner considers the optimal decisions under the worst-case scenario selected from a set of plausible alternative models. We find that the investment ambiguity and mortality ambiguity have substantially different impacts on the optimal decisions. Specifically, though the worst-case investment scenario depends only on the financial environment, the worst-case mortality scenario is determined by the intricate interplays between the wage earner's personal profile (e.g., health status, income dynamics, risk aversion, etc.) and the evolution of the financial market. What is more, the study of mortality ambiguity is also closely related to the value of life expectancy which can be positive and negative in general. Such a complicated theoretical structure underlying the risk of mortality ambiguity can sometimes even overturn the direction of its impacts on the optimal decisions. Our paper highlights the importance as well as the complexity for modeling ambiguity aversion in optimal retirement studies, which desires more serious and critical treatments from the community of actuarial professionals.

Thursday, August 9, 2018 Session 2C: Probability and Statistical Methods Time: 10:30 am – 12:00 pm Location: UCC 37 Chair: Brian Hartman, Brigham Young University 10:30 AM - 11:00 AM Title: The Laplace transform of the lognormal distribution Presenter: Justin Miles, York University Abstract: The lognormal distribution is widely used in mathematical modelling. For example, actuaries have used it for decades to model claim size for property and casualty insurance. A big open problem in this area is how to compute the distribution of the sum of independent lognormal random variables. While there is a vast literature on this subject, the question is still far from being resolved. In this talk I will focus on a Laplace-transform-based approach to this problem. I will explain the main ideas and the historyof this Laplace transform approach; demonstrate that one of the widely used approximations to the Laplace transform of a lognormal distribution is actually incorrect; discuss analytic properties of the Laplace transform and present two new series approximations. Then, with the help of these new results, I will demonstrate how one could calculate to a high precision the distribution of a sum of independent lognormal random variables in a very efficient manner.

11:00 AM - 11:30 AM Title: Ratemaking application of Bayesian LASSO with conjugate hyperprior Presenter: Himchan Jeong, University of Connecticut Abstract: The generalized linear model (GLM) is a well developed statistical model widely used in actu- arial practice for insurance ratemaking, risk classification, and even reserving. Recently, there has been an explosion of data mining techniques to refine statistical models for better vari- able selection procedure and for improved prediction accuracy. Such techniques include the increased interest in regularization techniques, or penalized likelihood, to achieve these goals. In this paper, we explore the idea of Least Absolute Shrinkage and Selection Operator (LASSO) in a Bayesian framework within a dependent frequency-severity model as a refinement to the dependent GLM developed by Garrido et al. (2016). The LASSO technique is a penalized least squares procedure developed by Tibshirani (1996) and is extended to a Bayesian interpreta- tion framework by Park and Casella (2008). We show that a new penalty function emerges if we further theoretically extend the Bayesian LASSO using conjugate hyperprior distributional assumptions. While this result has the ease of implementation for variable selection and predic- tion, we recognize that the use of least squares has been poorly viewed in insurance ratemaking. Instead however, we modify the setting to a penalized dependent GLM within this extended Bayesian LASSO framework. Within such framework, the regression estimates are derived by optimizing a penalized likelihood assuming a hyperprior distribution for the L1 penalty param- eter λ. This has the advantage of avoiding to use of ex-post cross-validation for the optimal λ. We calibrated our proposed model using an auto insurance dataset from a Singapore insurance company where we have observed claim counts and amounts from a portfolio of policyholders.

11:30 AM - 12:00 PM Title: Smoothing of ratemaking errors to identify spatial auto-correlation Presenter: Christopher Blier-Wong, Universite Laval Abstract: Until now, geomatic data has not been frequently used in actuarial ratemaking. The use of geographic data to describe the spatial context of an insured risk is an interesting avenue due to their high availability and volume. However, insurance companies may lack the data warehouse

architecture to deal with geomatic data. We propose to identify areas of spatial auto-correlation as a preliminary step in using external data sources to supplement ratemaking explanatory variables. We explore a methodology to identify spatial boundaries of areas exhibiting greater concentrations of incurred losses with spatial auto-correlation measures and unsupervised learning. Insurance data has heavy tailed severity and scarce count frequency, making it difficult to isolate a spatial surface from the ratemaking residuals. Local regression models such as kriging, kernel smoothing and Local Polynomial Regression are adapted to insurance data. A new response variable is introduced to ease implementation and a binning method by peril is applied to the smoothed risk surface to incorporate in a ratemaking algorith

Thursday, August 9, 2018 Session 2D: Financial Modeling I Time: 10:30 am – 12:00 pm Location: UCC 41 Chair: Marcos Escobar-Anel, Western University 10:30 AM - 11:00 AM Title: Risk selection using live textual data from the web for commercial underwriting Presenter: Jean-Thomas Baillargeon, Laval University Abstract: Risk underwriting has a crucial importance in an insurer risk profile over the time. Bad risk selection can correspond to financial hardship in the future. In order to support risk evaluation during underwriting, we have developed a framework that enables live extraction of web textual information. These extracted information are used to automatically classify a company into a specific risk profile, using insurer’s in-house classification scheme. We also have developed enhancement to current best practices for smaller data sets. These enhancements are 2 folds, an augmented text emphasis based on correlation between words and risk profile and a dynamic hierarchical classification for nested risk categories. In our presentation, we will be presenting our framework and enhancement to current best practices, using Google Places and Yellow Pages data to classify a company into it’s business occupancy group.

11:00 AM - 11:30 AM Title: Effect of Withdrawal Frequency on the Retirement Funds Presenters: Kris Nilsson and Kaitlyn Fleigle, Maryville University of St. Louis Abstract: When it comes to retirement planning, many factors contribute to a retiree’s withdrawal strategy in order to satisfy his or her financial needs. These include asset allocation, frequency of withdrawals, and the withdrawal rate. Formulating a combination of these aims to optimize the account’s longevity and reduce failure rate. We will focus on investigating the effects of withdrawal frequency and timing by considering both the 4% rule and maximum withdrawal rates. This will be conducted based on back- testing and Monte Carlo simulations.

11:30 AM - 12:00 PM Title: Assessing the financial viability of the Road Accident Benefit Scheme in South Africa Presenter: Coetzee Marais, University of Cape Town Abstract: An assessment is made of whether the combination of fixed benefits, relaxed claims eligibility criteria and a simpler claims administration process, as proposed in the Road Accident Benefit Scheme Bill of 2014, can be expected to lead to a solvent form of compulsory motor vehicle insurance in South Africa. It is estimated that, had the Road Accident Benefit Scheme (RABS) replaced the Road Accident Fund (RAF) on 1 April 2014 and continued to operate as a no-fault system of compensation, the RABS would not have been financially viable, although the financial position of the RABS would have been significantly healthier than that of the RAF as at 31 March 2017. This estimate is, however, subject to material uncertainty.Key-words: no-fault compensation, compulsory motor vehicle insurance, South Africa.

Thursday, August 9, 2018 Session 2E: Measuring and Modeling Risk Time: 10:30 am – 12:00 pm Location: UCC 60 Chair: Elias Shiu, University of Iowa 10:30 AM - 11:00 AM Title: Poissonian Potential Measures for Levy Risk Models Presenter: Di Xu, University of Nebraska Lincoln Abstract: This paper studies the potential (or resolvent) measures of spectrallynegative Levy processes killed on exiting (bounded or unbounded)intervals, when the underlying process is observed at the arrival epochs of anindependent Poisson process. Explicit representations of these so-calledPoissonian potential measures are established in terms of newly definedPoissonian scale functions. Moreover, Poissonian exit measures are explicitlysolved by finding a direct relation with Poissonian potential measures. Ourresults generalize Albrecher et al. (2016) in which Poissonian exitidentities are solved. As an application of Poissonian potential measures, weextend the Gerber-Shiu analysis in Baurdoux et al. (2016) to a (moregeneral) Parisian risk model subject to Poissonian observations.

11:00 AM - 11:30 AM Title: Stochastic approximation algorithms applications in variable annuities Presenter: Anne MacKay, Universite du Quebec a Montreal Abstract: Stochastic approximation (SA) algorithms have first been introduced in the 1950s as a method of solving fixed point or optimization problems when the objective function is unknown and can only be estimated via noisy observations. They have since been used extensively in statistics and engineering for various purposes such as parameter estimation and reinforcement learning. In this presentation, we first give a brief overview of the Robbins-Monro and Kiefer-Wolfowitz SA algorithms and their most important improvements. We then show how these algorithms can be used in the context of variable annuities (VA) to speed up calculations and to improve the precision of the results. The first example focuses on the fixed point problem of finding the so-called fair fee rate, when no closed-form expression is available for the present value of a VA contract. In the second example, we show that SA is a favourable alternative to least-squares regression when assessing optimal surrenders. Both examples are supported by numerical illustrations.

11:30 AM - 12:00 PM Title: Sign Patterns in Correlation Matrices Presenter: Phelim Boyle, Wilfrid Laurier University Abstract: The first principal component of the correlation matrix of stock returns can be used to construct a diversified portfolio with attractive risk-return properties. Generally this is a long-only portfolio but sometimes the portfolio contains short positions. These short positions can be anathema to some institutions because of their unlimited risk exposure so it is of interest to explore why they occur. They stem from the presence of negative correlations among stock returns. It has been shown that the short positions depend on the number, magnitude and location of the negative correlations. The ultimate aim is to derive the necessary conditions under which a general n-by-n correlation matrix with some negative entries has a strictly positive dominant eigenvector. To this end, it is helpful in classifying and interpreting the results to focus on groups of correlation matrices that form equivalence classes. These equivalence classes are generated using permutation matrices.

Thursday, August 9, 2018 Session 3A: Optimal Insurance Time: 1:15 pm – 2:45 pm Location: McKellar Room Chair: Wei Wei, University of Wisconsin- Milwaukee 1:15 PM - 1:45 PM Title: Optimal Insurance with Belief Heterogeneity Presenter: Mario Ghossoub, University of Waterloo Abstract: In Arrow’s classical problem of demand for insurance indemnification, a linear deductible sched- ule is optimal for an Expected-Utility (EU) maximizing decision maker (DM), if the premium depends on the indemnity’s actuarial value, if the DM and the insurer share the same probabilis- tic beliefs about the realizations of the random loss, and if neither party experiences ambiguity (Knightian uncertainty) about the realizations of this loss. Motivated by epistemic foundations and the decision-theoretic approach to subjective belief formation, we re-examine the problem of demand for insurance indemnification when the DM and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. Unlike the existing (albeit narrow) literature on belief heterogeneity in optimal insurance design, we do not impose conditions on the type or level of disagreement about probabilities. Rather, we provide a closed-form characterization of the optimal indemnity for any type or level of belief heterogeneity, even allowing for disagreement about zero-probability events. We show that there exists an event A to which the insurer assigns full probability (but not necessarily the DM), such that the optimal indemnity for the DM is a state-contingent deductible over A and full insurance over the complement of A. We then recover several results from the existing literature as special cases. Moreover, we introduce a measure of belief divergence and examine how the level of disagree- ment in beliefs affects the shape of the optimal indemnity. In particular, we show that the level of belief heterogeneity has an intuitive two-fold effect: the higher the level of divergence, the lower the DM’s perception of the likelihood of the event A (and hence the higher her perception of the likelihood of full insurance), and the higher the level of the state-contingent deductible, ceteris paribus. Finally, we show how our belief divergence measure leads to a belief divergence metric on the vector space of all probability measures defined on our initial measurable space. We study the topological properties of the hence defined metric space and their implications for our insurance problem.

1:45 PM - 2:15 PM Title: Pareto-Optimal Risk Sharing among insurers under Mean- Variance Criterion Presenter: Lyu Chen, University of Waterloo Abstract: In this paper, we consider a dynamic Pareto-optimal risk sharing problem under the time consistent mean-variance criterion. We allows n insurers to share an underlying risk process which is modelled by a Levy process. By solving the extended Hamilton- Jacobi-Bellman equation and utilizing the Lagrangian method, explicit form of the equilibrium retention function of each insurer is obtained. We find that the equilibrium retention functions are mixtures of the two most common risk sharing forms, namely, proportional strategy and excess-of-loss strategy. Thanks to their explicit forms, analytical properties of the equilibrium retention functions are carefully investigated. In the second part of the paper, we consider three extensions to the original model: risk sharing constraint to the insurers, financial investment opportunities, and insurers' ambiguity towards the underlying risk process. Equilibrium retention functions under these extended models

are also explicitly solved, and the impact of constraint, investment, and ambiguity to the retention functions are examined. 2:15 PM - 2:45 PM Title: On optimal reinsurance treaties under a cooperate game Presenter: Jiandong Ren, Western University Abstract: In this paper, we consider the optimal reinsurance policies as the result of a two-person cooperative game, where both parties in the negotiation are risk averse and are trying to maximize their expected utility. We incorporate information asymmetry of the two parties by assuming that they have different beliefs about distribution of the underlying losses.Two situations are considered: in the first one, premium is completely negotiable, whereas in the second one, the premium is determined by actuarial premium principles. For both situations, we first obtain the form of Pareto-optimal reinsurance policies and then the optimal policy in the Nash equilibrium as well as that in the Kalai-Smorodinsky equilibrium are studied.

Thursday, August 9, 2018 Session 3B: Education Updates from the SOA, CAS and CIA Time: 1:15 pm – 2:45 pm Location: UCC 146 Chair: Steve Kopp, Western University 1:15 PM - 1:45 PM Title: Society of Actuaries Education Update Presenter: Stuart Klugman, Society of Actuaries Abstract: The Society of Actuaries revised ASA curriculum is now underway. This presentation will focus on the new Statistics for Risk Modeling and Predictive Analytics exams. Additional topics of current interest will be discussed.

1:45 PM - 2:15 PM Title: Casualty Actuarial Society Education Update Presenter: Jeanne Crowell, Vice President - Admissions, Casualty Actuarial Society Abstract: The CAS will discuss Integrative Questions, the new Modern Actuarial Statistics exams, and recent technological developments. 2:15 PM - 2:45 PM Title: Canadian Institute of Actuaries Education Update Presenter: Marc Tardif, President-Elect, Canadian Institute of Actuaries Abstract: Topics will include Education Strategy, University Accreditation Program, Graduate Scholarship Program, and Education Activities

Thursday, August 9, 2018 Session 3C: P&C Insurance Time: 1:15 pm – 2:45 pm Location: UCC 37 Chair: Jay Vadiveloo, University of Connecticut 1:15 PM - 1:45 PM Title: Predictive analytics of insurance claims using multivariate decision trees Presenter: Zhiyu Quan, University of Connecticut Abstract: Because of its many advantages, the use of decision trees has become an increasingly popular alternative predictive tool for building classification and regression models. Its origins date back for about five decades where the algorithm can be broadly described by repeatedly partitioning the regions of the explanatory variables and thereby creating a tree-based model for predicting the response. Innovations to the original methods, such as random forest and gradient boosting, have further improved the capabilities of using decision trees as a predictive model. In addition, the extension of using decision trees with multivariate response variables started to develop and it is the purpose of this paper to apply multivariate tree models to insurance claims data with correlated responses. This extension to multivariate response variables inherits several advantages of the univariate tree models such as its distribution-free feature, ability to rank essential explanatory variables, and high predictive accuracy. To illustrate the approach, we analyze a dataset drawn from the Wisconsin Local Government Property Insurance Fund (LGPIF) which offers multi-line insurance coverage of property, motor vehicle, and contractors' equipments. With multivariate tree models, we were able to capture the inherent relationship among the response variables, and we found that the marginal predictive model based on multivariate trees was an improvement from that based on merely the univariate trees.

1:45 PM - 2:15 PM Title: Implementation of Dependence between Frequency and Severity in Bonus-Malus System Presenter: Rosy Oh, Ewha Womans University Abstract: A Bonus-Malus System (BMS) in auto insurance is a premium adjustment mechanism widely used in a posteriori ratemaking process to set the premium for the next time period based on the previous claim history of a driver. While independence between claim frequency and severity is key assumption in BMS, series of recent literature under various statistical models report the significant dependence between claim frequency and severity in auto insurance. In this paper, using the bivariate random effect model where the dependence between claim frequency and severity is introduced by copula based bivariate random effect, we illustrate how to combine the dependence structure into the current BMS and provide the analytical solution for the corresponding optimal relativities. The real data analysis and numerical examples are accompanied to assess the effect of dependence in BM system.

2:15 PM - 2:45 PM Title: Some observations on the time patterns in the surplus process of an insurer Presenter: Yang Miao, Western University Abstract: This project studies some patterns arising in the surplus process of an insurer. Using real-world data, we discovered that the purchasing process of an insurance policy and the corresponding claim process have seasonal fluctuations. Some special events, such as public holidays, also have impact on these processes. A preliminary analysis of the impact of these patterns on the surplus process is also conducted.

Thursday, August 9, 2018 Session 3D: Actuarial Topics I Time: 1:15 pm – 2:45 pm Location: UCC 41 Chair: Jean-Francois Begin, Simon Fraser University 1:15 PM - 1:45 PM Title: Blockchains: what they are, how they work, and their implications for the insurance industry Presenter: Arnold Shapiro, Penn State University Abstract: Ten years ago, an elusive cryptologist named Satoshi Nakamoto proposed a peer-to-peer electronic cash system called bitcoin, which would allow online payments to be sent directly from one party to another without intervention. The core technology behind bitcoin was the blockchain, a decentralized transaction and data management technology. It featured a distributed, immutable digital record system that was shared among many independent parties and could be updated only by their consensus. While blockchain started off as a core technology of bitcoin, it has emerged as an innovative tool with the potential to impact the way a number of online applications are designed. One of the most notable of which are full-fledged programs that are run on blockchains, called smart contracts, which are based on computerized transaction protocols that autonomously execute the terms of a contract. Smart contracts have been mentioned with respect to a number of insurance application areas, including contract enforcement, the streamlining of business transactions, customer engagement and satisfaction, fraud monitoring and detection, product development, and the handling of reinsurance contracts.The purpose of this presentation is to provide an overview of blockchains, including what they are and how they work, and their implications for the insurance industry.

1:45 PM - 2:15 PM Title: On Ordering Prospects by Insurance Premiums Presenter: Mostafa Mashayekhi, University of Nebraska-Lincoln Abstract: In this paper we consider total orders on sets of non-negative random variables implied by insurance premiums for full coverage, when the random variables may be considered as insurable risks. Such orderings may have useful applications when one is faced with two random prospects X and Y such that neither of the two prospects dominates the other by a form of stochastic dominance and one has to choose one of the two prospects without basing the selection on a single arbitrary utility function. We look at orderings given by different principles of premium calculation and their relations with stochastic orders such as the first degree stochastic dominance, the second degree stochastic dominance, and the stop-loss order. A discussion of cases when an ordering by a given principle of premium calculation does not preserve a form of stochastic dominance is presented.

2:15 PM - 2:45 PM Title: The Economics of the Secondary Market for Variable Annuities Presenter: Thorsten Moenig, Temple University Abstract: In this article, we demonstrate that a secondary market transaction for variable annuity (VA) policies has the potential to benefit all three parties involved: the original policyholder, the third-party investor, and in particular the insurance company. We argue that this is due to the present of market frictions such as taxes and acquisition expenses that induce each party to have a different valuation perspective, which could make a VA policy more attractive to the third-party investor than to the policyholder and to the insurer. Our findings thus offer insights to not only practicing actuaries in the VA business line, but also insurance regulators with regards to the supervision of the secondary VA market.

Thursday, August 9, 2018 Session: 3E Topic: Reinsurance Time: 1:15 pm – 2:45 pm Location: UCC 60 Chair: Xiaoming Liu, Western University 1:15 PM - 1:45 PM Title: Simulation of Correlated Levy Negative Binomial Processes for Quantitative Risk modelling Presenter: Maral Mazjini, University of Regina Abstract: In the context of quantitative risk modelling extremal dependencestructure between risk processes is one of the main concerns. Backwardmethods recently studied to construct and simulate correlated multi-variate Poisson processes turn out to be computationally ecient andallow to incorporate extremal correlation patterns. In this talk, we willdiscuss the construction and simulation of correlated Levy negative bi-nomial processes which are appealing models for over-dispersed countdata such as operational losses. A backward construction which relieson the conditional uniformity of the increment processes under a par- ticular setting will be presented in detail. The attainable correlationboundaries under forward and backward approaches will be compared.We will also discuss the use of a copula to have more flexible timecorrelation patterns.

1:45 PM - 2:15 PM Title: Optimal Investment and Reinsurance Strategies with Bayesian Learning Presenter: Jingyi Cao, University of Waterloo Abstract: In this paper, we study an insurer’s investment-reinsurance problem with partial information under a mean-variance criterion, where the stock’s expected return is modelled as an unobservable constant random variable, and the surplus process is a spectrally negative Levy process. By reducing the problem to an equivalent one with complete information, and solving an extended HJB equation, we obtain the explicit equilibrium investment-reinsurance strategy. Moreover, a comparison between the equilibrium strategy and its myopic counterpart is also conducted. Finally, some numerical illustrations are provided. This is a joint work with Professor David Landriault and Professor Bin Li.

2:15 PM - 2:45 PM Title: Optimal reinsurance considering synergy potential Presenter: Wenjun Jiang, University of Western Ontario Abstract: An important question in design of optimal reinsurance policies is how much can insurance company and reinsurance company gain through cooperation. In finance literature, when companies cooperate with each other, the possible increase in total expected utility or decrease in total risk is called synergy potential (Gerber and Pafum, 1998). In this paper, we study the form of Pareto optimal reinsurance policy that maximize the insurer’s and the reinsurer’s expected utilities, under the condition that the total risk, measured by distortion risk measures, is minimized. Multi-layer reinsurance policies are derived. Numerical examples are provided to show the practical implications of our results.

Thursday, August 9, 2018 Session 3F: Health, Retirement and Social Security Time: 1:15 pm – 2:45 pm Location: UCC 60 Chair: Shu Li, Western University 1:15 PM - 1:45 PM Title: Unsupervised Clustering with All Categorical Variables Presenter: Margie Rosenberg, University of Wisconsin - Madison Abstract: We present a case study to illustrate a novel way of clustering individuals to create groups of similar individuals where covariates are all categorical. Our method adapts to categorical data where there is no inherent order in the variable, like race. We use data from the National Health Interview Survey (NHIS) to form the clusters and apply these clusters for prediction purposes to the Medical Expenditures Panel Study (MEPS). Our approach considers the person-weighting of the surveys to produce clusters and estimates of expenditures per cluster that are representative of the US adult civilian non-institutionalized population. For our clustering method, we apply the K-Medoids approach with an adapted version of the Goodall dissimilarity index. We validate our approach on independent NHIS/MEPS data from a different panel. Our results indicate the robustness of the clusters across years and indicate the ability to distinguish clusters for the predictability of expenditures. 1:45 PM - 2:15 PM Title: A Multi-faceted Analysis of Solvency and Sustainability of the U.S. Social Security system Presenter: Ken Buffin, Buffin Foundation Abstract: The United States Social Security system is the focus of much public policy debate due to concerns over the effects of secular demographic changes and the challenges to the system's long-term financial sustainability. Previous work by the author presented at the 49th Actuarial Research Conference in 2014 contributed to these public policy issues by presenting a system of eight suitable objective actuarial assessments of financial stability, solvency and sustainability. This presentation to the 2018 Actuarial Research Conference will provide a continuation of previously published research by the author that will include an analysis of historical data and long-range actuarial projections for the U.S. Social Security system, with a specific focus on the 75-year and 25-year financial projections published by the Social Security Trustees between 1991 and 2017. A comprehensive analysis of the secular trend in metrics for the system's actuarial solvency over this period will be presented together with a corresponding analysis of the secular trend in the requisite equilibrium payroll tax rate that would be necessary to maintain the system's actuarial solvency. Also to be presented is a specific policy proposal for maintaining actuarial solvency by means of an automatic procedure for dynamic parametric adjustments to the payroll tax rate subject to certain constraints to ensure fairness and affordability.

2:15 PM - 2:45 PM Cancelled

Thursday, August 9, 2018 Session 4A: Health Topics Time: 3:15 pm – 4:45 pm Location: McKellar Room Chair: Margie Rosenberg, University of Wisconsin – Madison 3:15 PM - 3:45 PM Title: Measuring and analyzing Individual Healthy Life Expectancy Presenting Author: Jeyaraj (Jay) Vadiveloo, University of Connecticut Abstract: Life expectancy (LE) is a well understood and studied concept in actuarial science and the medical/nutrition literature. We have decided to focus on Healthy Life Expectancy (HLE) and how to manage HLE. By default, the difference between LE and HLE would represent the period of time an individual is living and in an “unhealthy” state. The Unhealthy Life Expectancy (ULE) is simply LE minus HLE. Managing HLE (and ULE) has significant implications for retirement financial planning, LTC and life annuities product design, and individual wellness measurement. Research Goals Our research intends to accomplish the following: Provide a formal definition of “unhealthy” (and “healthy”) states of living Develop a model to calculate HLE, LE and ULE based on actuarial assumptions of annual healthy survivorship rates, incidence rates of disability and “unhealthy” survivorship rates Use established research findings in Nutrition Science to develop a predictive model and a web-based application to study the impact of the following on healthy LE: a. Changes in diet and nutritional habits b. Impact of exercise c. Impact of lifestyle changes (e.g. greater socialization, marriage, divorce, death of a spouse, etc.) Apply the healthy life expectancy concept to determine:

• Retirement financial planning spending patterns • The optimal deferral period for purchasing a deferred long term care policy • The optimal benefit period for LTC coverage • A health score for evaluating individual wellness

3:45 PM - 4:15 PM Title: Predicting High-cost Members in the HCCI Database Presenting Author: Brian Hartman, Brigham Young University Abstract: Using the Health Care Cost Institute data (approximately 47M members over 7 years) we examine which characteristics best predict and describe high-cost members. We find that cost history, age, gender, and prescription drug coverage all predict high-costs, with cost history being the most predictive. We also compare the predictive accuracy of logistic regression to extreme gradient boosting and find that the added flexibility of the extreme gradient boosting improved the predictive power. Finally, we show that with our extremely unbalanced classes, oversampling the minority class provides a better predictive model than undersampling the majority class or using the training data as is. Coauthors: Rebecca Owen and Zoe Gibbs 4:15 PM - 4:45 PM Title: Doubly Enhanced Annuities and the Impact of Price and Quality of Long Term Care on Retiree Decisions Presenter: Colin Ramsay, University of Nebraska – Lincoln Abstract: The relatively small size of voluntary immediate life annuity markets seemingly contradicts Yaari's (1965) assertion that, under certain conditions, utility maximizing retirees should annuitize all of their wealth upon retirement. This apparent contradiction

contributes to what is called the ``annuity puzzle'' because it. The main explanations for the annuity puzzle include adverse selection, bequest motives, and retirees' fear of health shocks. Because of insurers' fear annuitants may live well beyond their life expectancy, voluntary immediate life annuities are priced in a manner that make them unattractive to the general retiree population. The objective of this paper is to develop the theoretical basis for an annuity product that is attractive to the general retiree population, thus expanding the size of voluntary immediate life annuity markets. Such a product partly exists and is called an enhanced (substandard or impaired life) annuity because it partly solves the problem of adverse selection. Enhanced annuities are medically underwritten to provide greater annual benefits to annuitants with shorter than average life expectancy. Unfortunately, enhanced annuities do not tackle the problem of long term care during the retirement years. Thus we develop a hybrid annuity called a doubly enhanced annuity that protects against adverse selection, provides a long term care benefit, and satisfies a bequest motive. A major contribution of our research is the introduction of quality of long term care received and its impact on future mortality and morbidity. Specifically, retirees must decide on the level of quality of care they can afford over their lifetime. We provide a numerical example showing the optimal choice of quality of care for various designs of doubly enhanced annuities.

Thursday, August 9, 2018 Session 4B: Pensions and Retirement II Time: 3:15 pm – 4:45 pm Location: UCC 146 Chair: Yang Shen, York University 3:15 PM - 3:45 PM Cancelled

3:45 PM - 4:15 PM Title: Retirement Consumption, Risk Perception and Planning Objectives Presenter: Saisai Zhang, University of Waterloo Abstract: In this talk, we present the results from a 2016 Canadian retirement study on retirement consumption, risk perception and planning objectives. The study is conducted through an online survey of 1,000 randomly selected Canadian pre- retirees and retirees. The objective of the survey is to obtain a more complete picture of retirement experiences and objectives of Canadians, and to compare and contrast them with assumptions made in models of lifetime portfolio selection. We are interested in three key areas. The first is the difference between expectations and experience among Canadian retirees, in particular, relating to the areas of longevity, consumption, and risk and variability of income. The second area relates to the current level of wealth in retirement, or savings pre-retirement. The third area addresses preferences and risk aversion, in particular in assessing whether the emergent preferences are well-represented by commonly employed utility functions.

4:15 PM - 4:45 PM Title: What the Heck is a HECM? Presenting Author: Stephanie Lee, University of California – Santa Barbara Abstract: Home Equity Conversion Mortgages (HECMs) are loans made to senior borrowers against the value of their home. The U.S. Federal Housing Administration (FHA) insures HECMs through Mortgage Insurance Premiums (MIPs) paid by borrowers. The HECM fund is currently underfunded. Premiums have recently been increased. Our hypothesis is that the increase in premiums will return the fund to solvency over time. We created a model to simulate the gains and losses of the HECM fund, assuming the current population. The model allows the user to test the FHA’s liability by adjusting assumptions to simulate different borrower profiles, drawdown strategies, FHA regulation changes, and economic environments. On balance, we find that the new premium levels are sufficient to fund the liabilities implying that over time the fund may return to solvency or show a surplus under the shifting population dynamics.

Thursday, August 9, 2018 Session 4C: Actuarial Modeling II Time: 3:15 PM – 4:45 PM Location: UCC 37 Chair: Jed Frees, University of Wisconsin – Madison 3:15 PM - 3:45 PM Title: On Bivariate Kumaraswamy- Distorted Copulas Presenter: Ranadeera Samanthi, Central Michigan University Abstract: We propose families of bivariate copulas based on the Kumaraswamy distortion of existing copulas. With the additional two parameters in the Kumaraswamy distribution, the induced copulas permit more flexibility in tail behaviors. The framework employed in this work provides a method for generating Archimedean copula models. Two theorems linking the original tail dependence behaviors and those of the distorted copula are derived for distortions that are asymptotically proportional to the power transformation in the lower tail and to the dual-power transformation in the upper tail. We also derive explicit formulas for the Kendall's tau coefficient, tail order parameters and tail order functions for the induced copulas when Gumbel, Clayton, Frank and Galambos are distorted. Authors: Ranadeera Samanthi and Jungsywan Sepanski

3:45 PM - 4:15 PM Title: A global approach to modeling flood risk diversification for (re) insurers Presenter: David Carozza, Universite du Quebec a Montreal Abstract: Flood is a key driver of economic and insured catastrophic losses throughout the world, as well as a leading cause of catastrophe- related death in developing countries. From 2000-2016, flooding caused an average of USD44 and USD8 billion in economic and insured losses, respectively, at the global scale. Due to mounting losses and the complexity of insuring flood risk, (re)insurance and a variety of insurance linked securities are used for flood risk management. For a (re)insurer writing flood risk, diversification requires an appreciation of the environmental factors that set the spatial and temporal characteristics of flood frequency and severity. While flood is often studied in particular rivers or hydrological basins, a global modeling approach is feasible because floods can occur in any location where a river is present. Moreover, from year to year, spatial patterns of flood are strongly influenced by large-scale climate patterns such as the El-Nino Southern Oscillation, which perturbs precipitation and temperature over a large part of the globe. The current generation of global flood models can now represent small-scale features of flooding within towns and neighborhoods of cities. While such hydrological models have provided important advances to local flood risk assessments, they are not currently computationally or conceptually appropriate for use in the large-scale risk assessments that are relevant to (re)insurers. To engage this problem, we present a new database of an extensive set of environmental variables that are integrated over hydrological basins. Then, based on a global database of large riverine floods dating from 1985 to the present, the Dartmouth Flood Observatory database, we develop preliminary models of global flood risk measured in terms of the area affected by flood. We then analyze diversification and concentration of flood risk over the globe from the perspective of a (re) insurer. 4:15 PM - 4:45 PM Title: Estimating Veterans' Health Benefit Grants Using the Generalized Linear Mixed Cluster -Weighted Model with Incomplete Data Presenter: Petar Jevtic, Arizona State University Abstract: In this work, a novel application of the Generalized Linear Mixed Cluster-Weighted Model is given in the context of right-censored observations. The motivating problem is forecasting U.S. veteran dental benefit grants based on the data set provided by North Dakota Department of Veterans Affairs (DVA). In the United States, veterans are granted various benefits on the federal and state level through DVA. These grants positively impact the quality of veterans' lives and

proper understanding of true needs is of importance for policymakers. Historically, amounts of dental grants available have varied. Thus, the individual grants at different times were capped at different levels. This poses considerable modelling and estimation challenge successfully dealt with by the proposed methodology. Here, we derive maximum likelihood parameter estimates using the appropriately modified EM algorithm. Among beneficiaries, we identify three distinct clusters and forecast their dental grant needs.

Thursday, August 9, 2018 Session 4D: Financial Modeling II Time: 3:15 PM – 4:45 PM Location: UCC 41 Chair: Mary Hardy, University of Waterloo 3:15 PM - 3:45 PM Title: Portfolio Optimization under Solvency II Constraints. Presenter: Marcos Escobar-Anel, Western University Abstract: In the current low interest-rate and highly-regulated environment investing capital e?ciently is one of the most important challenges insurance companies face. Certain quantitative parts of regulatory requirements (e.g. Solvency II capital requirements) result in constraints on the investment strategies. This paper mathematically describes the implications of Solvency II constraints on the investment strategies of insurance companies in an expected utility framework with a focus on the market risk module. For this constrained expected utility problem, we de?ne a two-step approach that leads to closed-form approximations for the optimal investment strategies. This proposal circumvents the technical di?culties encountered when applying the convex duality approach or the theory of viscosity solutions. The investment strategies found using the two-step approach can be understood as the optimal investment strategies for constraint problems according to Solvency II. The impact of such constraints on the asset allocation and the performance of these strategies is assessed in a numerical case study.

3:45 PM - 4:15 PM Title: Utility maximization under regime -switching: a Laplace method Presenter: Adriana Ocejo, UNC Charlotte Abstract: In this talk, we present an explicit solution to the problem of power utility maximization from terminal wealth in which an agent optimally builds her portfolio by investing in a bond and a risky asset, the latter following regime-switching dynamics. A regime is understood as a state of the economy. We deduce the associated Hamilton-Jacobi-Bellman equation to construct the solution and the optimal trading strategy, this part is standard in optimization theory. The problem is verifying that the HJB equation admits classical solutions, which is typically overlooked in the literature. We verify optimality by showing that the value function is the unique constrained viscosity solution of the HJB equation. Also, we show how to explicitly compute the value function by Laplace transform methods and illustrate the method with the two- and three-states cases.

4:15 PM - 4:45 PM Title: Multivariate Scenario Reduction-- Applied to Segregated Funds Guarantees Presenting: Yvonne Chueh, Central Washington University Abstract: A segregated fund, as a mutual fund with insurance guarantee, is a valuable estate planning tool to protect from creditors or probate. The gross sales was about 12.4 billion in 2015, 16.8% increase from 2014 and the estimated total assets reached $116 billion in 2017. In practice, calculations for dynamic hedging models for segregated funds are computationally intensive since the latter are nested stochastic scenario calculations. In this paper, we propose an approach to reduce calculation time by adapting Chueh’s scenario reduction algorithm to dynamic hedging models for segregated funds for guaranteed minimum maturity benefit (GMMB). We also show that using graphical processing units to calculate the scenario reduction algorithm significantly lowers the calculation time. In addition, a comparison of Chueh’s scenario reduction with conventional clustering algorithms and time series clustering, respectively, was conducted using a real world segregated fund model.

Thursday, August 9, 2018 Session 4E: Mortality/Longevity Time: 3:15 PM – 4:45 PM Location: UCC 60 Chair: Chris Groendyke, Robert Morris University 3:15 PM - 3:45 PM Title: The pricing of a guaranteed minimum maturity benefit under a regime-switching framework Presenter: Yixing Zhao, University of Western Ontario Abstract: Over the last few decades, more sophisticated products have emerged in the global insurance markets in response to the new era of living longer in retirement. Policy holders are now able to enjoy the benefits of longevity/mortality protection whilst taking advantage of opportunities in the investment markets. Insurers incorporate payment guarantees in new insurance products known as equity-linked contracts whose values are dependent on the prices of risky assets. In particular, a guaranteed minimum maturity benefit (GMMB) is embedded in many equity-linked contracts. We develop a modelling framework to support the valuation and risk management of a GMMB in segregated fund contracts although in this research we would only address pricing and parameter estimation considerations. Hidden Makov models (HMMs) are constructed for the joint evolution of the stock price index, interest rate, and mortality rate. The dependence between these risk factors are modelled and characterised explicitly. We assume that the price index is a Markov-driven geometric Brownian motion, and both the interest and mortality rates have Markov-modulated affine specifications. A series of measure changes is employed to obtain a semi-closed form solution for the price of the GMMB. A Fourier-transform method is applied to approximate the prices more efficiently. HMM-based recursive filters are derived for the calibration of models to historical data. Our numerical work demonstrates the accuracy and efficiency of the proposed valuation method and gives a comprehensive analysis on how the three risk factors affect the GMMB prices.

3:45 PM - 4:15 PM Title: A Further Investigation of Longevity Greeks: Dynamic Delta, Leverage Effect and Security Structures Presenter: Kenneth Zhou, University of Waterloo Abstract: Longevity Greeks have been shown to be useful for calibrating index-based longevity hedges. In this paper, we contribute three extensions of longevity Greeks. First, we incorporate leverage effect (i.e., the relationship between volatility and the direction of mortality shocks) into longevity Greeks by considering asymmetric GARCH models for the evolution of mortality. Second, we introduce an alternative version of longevity vega, which is more robust with respect to the estimate of the GARCH parameter. The improved robustness enables users to apply this Greek to a broader range of fitted models. Third, we propose a new longevity Greek called ‘dynamic delta’, which is derived using total derivatives (instead of partial derivatives). As total derivatives are being used, a dynamic delta incorporates both the direct and indirect effects of a shock to the stochastic process driving the evolution of mortality. We use real mortality data to illustrate the importance of incorporating leverage effect and the benefit of using dynamic delta over the original version of longevity delta. We also demonstrate how the effectiveness of a Greek longevity hedge may be related to the structure of the hedging instrument used.

4:15 PM - 4:45 PM Title: Spatial filtering approach to mortality modeling Presenter: Kyran Cupido, Arizona State University Abstract: Within the field of spatial analysis, spatial filtering has emerged as a powerful mod- eling technique. In this work, for the first time in actuarial literature, this approach is introduced in the mortality modeling context. Specifically, the aim of this research is to identify patterns in the spatial

distribution of mortality rates for the sixty-five and older age group at the county level for the continental United States. The analysis carried out pertains to the spatial autocorrelation of these rates over time. The spatial filtering methodology was applied to uncover the latent spatial patterns which remained consistent across the years in the study. Preliminary results show the existence of spatial depen- dencies leading to an accompanying spatial filter. This may prove useful to practically introduce a spatial domain into existing traditional mortality models.

Friday, August 10, 2018 Session 5A: Plenary Session II Time: 9:00 AM – 10:15 AM Location: McKellar Room Chair: Bruce Jones, Western University 9:00 AM – 9:05 AM Announcements

9:05 AM – 9:15 AM IAA Mortality Working Group Resources, by Brian Ridsdale, IAA Working Group

9:15 AM – 10:15 AM Keynote Presentation Title: Mitigation of insured losses to extreme weather: Can we build houses to resist tornadoes? Presenter: Greg Kopp, Western University Abstract: Economic and insured losses due to extreme weather continue to rise around the globe. In North America, losses due to wind storms are significant because of hurricanes, tornadoes and other types of storms. Even though annual average losses caused by tornadoes are similar to those from hurricanes, design of buildings to resist the impacts of tornadoes has not been considered, except for high-consequence infrastructure such as nuclear reactors. This is beginning to change. With the realization that about 95% of tornadoes are EF-2 or less, with wind speeds equivalent to major hurricanes, several communities are now developing building code requirements which consider tornadoes. The presentation explores what is required to make wood-frame houses resilient to tornadoes for these levels of tornadoes, along with what kind of loss reduction could possibly be achieved.

Friday, August 10, 2018 Session 6A: Plenary Session III Time: 10:45 AM – 12:00 PM Location: McKellar Room Chair: Stephen Camilli, ACTEX Learning 10:45 AM – 10:55 AM Society of Actuaries International Section, by Ken Seng Tan, University of Waterloo

11:00 AM – 12:00 PM Keynote Presentation Title: The impact of demographic changes and labor markets malfunctioning on pay-as-you-go pension systems: the case of Colombia Presenter: Santiago Montenegro, Asofondos Abstract: The aging population has turned into a risk for the sustainability of pay-as-you-go social security systems, in which young people pay the elderly´s pensions and/or a part of the national budget has to be spent on pensions payments. But, apart from demography, an urgent redesigning of the pension systems is required due to the malfunctioning of labor markets characterized by the existence of a large section of workers who do not make pension contributions -due to unemployment or to informality or both. As a result, coverage is low, pension contributions are also low, and systems become unfeasible. The discussion is mainly illustrated with data of the Colombian economy.

Friday, August 10, 2018 Session 7A: InsurTech Time: 1:15 PM – 2:45 PM Location: McKellar Room Chair: Ben Marshall, Society of Actuaries 1:15 PM – 2:00 PM Invited Presentation Title: InsurTech: New Products, Technology and Innovation Presenter: Ron Stokes, Ernst & Young 2:00 PM – 2:45 PM Invited Presentation Title: InsurTech is Applied Insurance Research Presenter: Don Mango, Innovensure Advisory Solutions LLC

Friday, August 10, 2018 Session 7B: Cyber Risk Time: 1:15 PM – 2:45 PM Location: UCC 146 Chair: Jiandong Ren, Western University 1:15 PM – 2:00 PM Invited Presentation Title: A Fundamental Approach to Cyber Risk Insurance Presenter: Stefan Laube, PwC Germany Abstract: This presentation provides a framework for actuaries to think about cyber risk. First, I propose a differentiated view on cyber versus conventional risk by separating the nature of risk arrival from the target exposed to risk. Second, I identify ways to rigorously model cyber risk, including its driving factors. This is a prerequisite for establishing a deep and stable market for cyber risk insurance.

2:00 PM – 2:45 PM Invited Presentation Title: A Fundamental Approach to Cyber Risk Analysis - A Practitioner's Perspective Presenter: Ben Goodman, 4A Security & Compliance Abstract: Following Stefan Laube's presentation "A Fundamental Approach to Cyber Risk Insurance", Ben will share relevant elements from cases he has worked on as a cyber security practitioner. Ben is the founder and CEO of 4A Security & Compliance, a firm that conducts cyber security assessments, breach response and helps organizations mount cyber security defenses. His unique perspective is also informed by his background in insurance and risk management as well as three decades working in IT. Ben's presentation will dovetail with Stefan's, painting a rich picture of real-world cyber risk analysis that ranges from the board room, through the enterprise down into the dark web and back out to the world of cyber insurance.

Friday, August 10, 2018 Session 7C: Distributions and Dependence Time: 1:15 PM – 2:45 PM Location: UCC 37 Chair: Peng Shi, University of Wisconsin-Madison 1:15 PM - 1:45 PM Title: Moment-Based Density Approximation Techniques as Applied to Heavy-tailed Distributions Presenter: John Sang Jin Kang, University of Western Ontario Abstract: Several advances are proposed in connection with the approximation and estimation of heavy-tailed distributions. First, we focus on approximating heavy-tailed distributions, such as the Pareto, Student-t and Cauchy, which only possess a finite number of moments, if any. It is explained that on initially applying the exponential tilting technique to such density functions, one can then utilize a certain moment-based technique whereby the tilted density function is expressed as the product of a base density function and a polynomial adjustment. Such approximation methodology can be further extended to heavy-tailed symmetric distributions by applying a symmetrization technique. Secondly, on applying a transformation to the variables so that their supports become compact or simply truncating them, one can express the density approximants associated with the modified distributions as polynomials. Finally, it is shown that we can utilize the proposed density approximation approach in the context of density estimation, in which case sample moments are employed in lieu of exacts moments. Heavy-tailed actuarial data sets are used to illustrate the proposed methodology. 1:45 PM - 2:15 PM Title: On the Class of Tail Dependence Matrices Generated by Commonly Used Copula Families Presenter: Siyang Tao, The University of Iowa Abstract: The tail dependence coefficient is a bivariate measure of dependence in the tails, and the tail dependence matrix (TDM) is the array of such bivariate measures corresponding to a randomvector. A TDM serves as a measure of multivariate tail dependence. It is known that the space of TDMs corresponding to d-dimensional random vectors is a polytope with exponential in dnumber of facets and vertices. In this talk, we will discuss some results that describe the subset of TDMs generated by some popular family of copulas; in some cases this subset is shown tobe a surprisingly small part of the whole space of TDMs. For high dimensional cases, it could be proved that the subsets have no volume. This suggests another dimension along which toevaluate copula families for practical use. 2:15 PM - 2:45 PM Title: Dependence within micro-level model for loss reserving Presenter: Roxane Turcotte, Laval University Abstract: In their daily practice, property and casualty companies are subject to a number of solvency constraints. In a nutshell, they must predict, with the highest accuracy, future claims based on past observations. The majority of existing models can be divided into two categories, micro- or macro-level, depending on the granularity of the underlying dataset. The latter have been widely developed by researchers and successfully applied by practitioners for several decades. The former have been studied for few years but actual use is very rare despite the many advantages of these methods. In this talk, we address the general question of loss reserving, and we contrast micro- and macro-level paradigms. More specifically, we consider the model introduced by Pigeon et al. (2013) and a micro-level dataset from a Canadian insurance company to study the dependence that can exist between many components of the development of a claim: reporting delay, time between two payments, number of payments, severity of the first payment, etc. To capture the dependence, we apply multivariate elliptical distributions, as well as copula models. This latter approach allows us to consider a wide variety of distributions for the marginal and for the dependence structure. We

discuss estimation procedures and we use simulations to obtain the predictive distribution of the total reserve amount. Finally, we quantify the risk associated to the reserve.

Friday, August 10, 2018 Session 7D: Actuarial Topics II Time: 1:15 PM – 2:45 PM Location: UCC 41 Chair: David Stanford, Western University 1:15 PM - 1:45 PM Title: Big Data, Small Talk Presenters: Benjamin Ku and Rahul Narula, University of California, Santa Barbara Abstract: The purpose of this project is to help an auto and homeowners’ insurance company improve their customer service, make call center operations more efficient, and reduce costs by analyzing their customer calls. Text mining methods such as topic modeling and sentiment analysis are used to study roughly 100,000 non-claim customer calls from the last year. These models provide insight into what customers call about and how they feel during their calls, allowing the company to adjust their processes and make improvements accordingly. Results show the most frequent topics of calls and how customer sentiment differs between topics.

1:45 PM - 2:15 PM Title: Eigen Portfolio Selection: A Robust Approach to Sharpe Ratio Maximization Presenter: Danqiao Guo, University of Waterloo Abstract: This paper shows how to pick optimal portfolios by modulating the impact of estimation risk in large covariance matrices. The portfolios are selected to maximize their Sharpe ratios. Each eigenvector of the covariance matrix corresponds to a maximum Sharpe ratio (MSR) portfolio for a different set of expected returns. Assuming that the portfolio manager has views on the future expected returns, a portfolio consistent with her views can be approximated by the first few eigenvectors of the sample covariance matrix. Since the estimation error in a large sample covariance matrix tends to be most severe in the eigenvectors associated with the smallest eigenvalues, the elimination of the tail eigenvectors reduces estimation error. We substitute the vector of expected excess returns by its lower-dimensional approximation so that the MSR portfolio is not contaminated by the estimation errors in the tail. To seek a balance between the approximation error and the estimation error, we set a tolerance limit for the former and make best efforts to control the latter. We further introduce a more general spectral selection method, which uses non-consecutive eigenvectors to approximate the expected excess returns. According to simulation and real-data studies, the advantage of the spectral selection method becomes apparent when the number of assets is large compared with the sample size. 2:15 PM - 2:45 PM Title: Ruin, the R_n class of distributions and total dividends Presenter: Ruixi Zhang, University of Western Ontario Abstract: We investigate a class of Sparre-Andersen risk processes in which the inter-claim times

are distributed. A key property of the class is given as a system of equations. This property allows the derivation of a new form of integro-differential equation, satisfied by a probability concerning the maximum surplus before ruin. The solution to this new integro-differential equation can be obtained by a standard technique that yields a defective renewal equation. We also provide

examples involving claim sizes as well as an application to the total dividends paid under a threshold strategy.

Friday, August 10, 2018 Session 7E: Topics in Life Insurance Time: 1:15 PM – 2:45 PM Location: UCC 60 Chair: Michael Sherris, UNSW Sydney 1:15 PM - 1:45 PM Title: Modeling Obesity Prevalence for the US Population Presenter: Tatjana Miljkovic, Miami University Abstract: Modeling and projecting the obesity prevalence have an important implication in the evaluation of mortality risk. A large volume of literature exists in the area of modeling mortality rates, but very few models have been developed for modeling obesity prevalence. We developed a stochastic model for modeling the obesity prevalence that accounts for an age and period effect as well as a cohort effect. We model the obesity prevalence for the United States population, aged 23-90, during the period 1988-2012. Forecast is validated in comparison to the actual data for the period 2013-2015.

1:45 PM - 2:15 PM Title: Equity Indexed Universal Life Insurance in College Funding Presenter: Zhixin Wu, DePauw University Abstract: Equity Indexed Universal Life (EIUL) is a variation of whole life insurance which carries a death benefit component and a cash value component. The popularity of EIULs has been growing quickly in recent years after the 2008 financial crisis. However, its long-term viability can’t be directly verified since no public data of EIULs is available to check its historical performance. This paper examines the performance of the EIULs as an alternative source of college education funding compared with the popular 529 college-savings plans. The actuarial pricing model of EIUL and the stochastic models for market variables like the stock market return, interest rate and option are built to simulate the future cash flows of EIULs and the 529 college-savings plans. The analysis of the two funding solutions shows that the EIULs is a reasonable way to fund the college education compared to the 529 college- savings plan when used appropriately.

2:15 PM - 2:45 PM Cancelled

Friday, August 10, 2018 Session 8A: Human Sustainability Time: 3:15 PM – 4:45 PM Location: McKellar Room Chair: Ben Marshall, Society of Actuaries 3:15 PM - 4:00 PM Invited Presentation Title: Climate Change (Actuaries Climate Index) Presenter: Steve Kolk, Kolkulations and Actuaries Climate Index Working Group Abstract: This presentation will give an overview of the Actuaries Climate Index (ACI) and the Actuaries Climate Risk Index (ACRI). I will will illustrate the ACI/ACRI and show how changing climate risks affect drought and crop risks.

4:00 PM - 4:45 PM Invited Presentation Title: Food - A Key to Sustainability? Presenter: Caterina Lindman, Actuaries Climate Index Working Group Abstract: Food is one of life's necessities. Our food systems are complex, and we devote a lot of resources, time and energy in growing, processing, transporting, cooking and serving food. This talk will give an overview of our food system within the context of resource use, outcomes and sustainability. Some ideas will be presented on how our food system can be transformed to reduce the use of resources, mitigate risk, and have better outcomes.

Friday, August 10, 2018 Session 8B: Mortality Improvement Time: 3:15 PM – 4:45 PM Location: UCC 146 Chair: Michael Stinchcombe, London Life 3:15 PM - 4:00 PM Invited Presentation Title: Recent developments in longevity, internationally Presenter: Brian Ridsdale, IAA Mortality Working Group Abstract: We know US and UK are seeing a slowdown - Where else - and why? What do we know about the causes and drivers of change? Are these indications a trend or a blip? Are there similarities internationally? What are demographers and actuaries doing?

4:00 PM - 4:45 PM Invited Presentation Title: Difference in mortality by socio-economic status: how much, why and is it getting better? Presenter: Assia Billig, Office of the Superintendent of Financial Institutions (Canada)

Friday, August 10, 2018 Session 8C: Statistical Methods Time: 3:15 PM – 4:45 PM Location: UCC 37 Chair: Vytaras Brazauskas, University of Wisconsin – Milwaukee 3:15 PM - 3:45 PM Title: Data mining techniques for actuaries: an overview Presenter: Banghee So, University of Connecticut Abstract: Data mining involves the computational process of exploring and analyzing large amounts of data to uncover hidden and useful information. Such information is useful to process and efficiently reduce data into a more summarized, analytical representation. The ultimate goal of data mining is to be able to deliver predictive models applicable to new data. Predictive modeling is increasingly becoming an important function of an actuary in all areas of insurance: life, health, pensions, property and casualty. In this survey article, we explore and describe the data mining tasks associated with supervised and unsupervised learning. There are generally four primary data mining tasks: association rule learning, clustering, classification, and regression. With each data mining task, we illustrate, using real data whenever available, its potential applications in actuarial science and in different areas of insurance. We further demonstrate the usefulness of these data mining techniques for actuaries to perform predictive analytics. Additionally, we briefly describe the emerging development of a new class of machine learning algorithms called deep structured learning. This is joint work with Professor Emiliano A. Valdez and Professor Guojun Gan, both from the University of Connecticut.

3:45 PM - 4:15 PM Title: Shared Random Effect Models for Frequency and Severity of Forest Fires Presenter: Devan Becker, University of Western Ontario Abstract: In this work, we have created a model for the random sum of random variables where the number and the burn area of forest fires are linked by a random effect. The value of this random effect will influence both the number of forest fires in a given day and the burn area of all of the forest fires that day. With the addition of a loading parameter, this model can indicate whether periods of high or low fire load are associated with small or large fires, or any combination thereof. The random effects framework accounts for unobserved variables that might affect both the ignition probability and the burn area, such as fluctuations due to El Nino. This joint modeling framework is easy to implement and can be used for any distribution of the number and burn area of fires, with the random effect acting as a dispersion parameter. The use of Bayesian estimation allows for an easy test of the dependence between the count and burn area models. While our focus is on fire science, this model is an extension of the loss modeling framework, where the frequency and severity are often assumed to be independent. It is straightforward to incorporate a random effect into the commonly used hurdle model for counts and Gamma GLM model for claim amounts. This will allow researchers to determine when there is a strong correlation between counts and claim amounts and to characterize this dependence. 4:15 PM - 4:45 PM Title: Efficient Nested Simulation for CTE of Variable Annuities Presenter: Ou (Jessica) Dang, University of Waterloo Abstract: For valuation of Variable Annuity contracts with a dynamic hedging program using Monte Carlo methods, nested simulation is often required. The process is computationally challenging, sometimes prohibitively so. We propose a simulation procedure for estimating the Conditional Tail Expectation (CTE) of liabilities of a Variable Annuity dynamic hedging strategy. In a CTE calculation, tail scenarios are most relevant. Thus, correctly identifying those scenarios would greatly improve the efficiency in a nested simulation. The proposed procedure takes advantage of

the special structure of the CTE by first identifying a small set of potential tail scenarios using only the first tier of simulation, following the proxy approach. We then focus the simulation budget on only the identified tail scenarios. We also study the CTEs estimated by nested simulations as concomitants of the order statistic of the proxies. We analyze statistics of the rank of such concomitants, and construct confidence intervals to ensure the tail of the liability distribution is sufficiently covered in the proxy tail scenarios. We conduct extensive numerical experiments on different guarantee types and different stochastic stock return dynamics. The numerical results show that, when given a fixed simulation budget, the proposed procedure can improve the accuracy of CTE estimation by an order of magnitude compared to a standard nested simulation.

Friday, August 10, 2018 Session 8D: Financial Modeling III Time: 3:15 PM – 4:45 PM Location: UCC 41 Chair: Anne MacKay, Université du Québec à Montréal 3:15 PM - 3:45 PM Title: Hedging of Dynamic Withdrawal Guarantees of Variable Annuities in the Presence of Basis Risk Presenter: Zhiyi Shen, University of Waterloo Abstract: The hedging of guaranteed withdrawal benefits embedded in the variable annuities (VAs) has raised great interests of the academics over the past decade or so. Due to the limited liquidity of the policy fund, the hedger in practice chooses highly liquid asset as the hedging instrument, which in turn gives rise to the basis risk. However, as yet the studies on the hedging strategies of these VA riders in the presence of basis risk are surprisingly sparse. This paper establishes a unified framework of hedging dynamic withdrawal benefits in VAs by seriously taking account of basis risk and thus provides one resolution to the inevitable problem faced by the practitioners. In contrast to the local risk minimizing approach widely studied in the literature, we restrict the hedging strategy to be self-financing and formulate the hedging problem under a stochastic optimal control framework. Under certain limiting scenarios such as a high policy fund value and depletion of investment account, we manage to obtain analytical solutions to the corresponding optimal hedging strategies. In the general case, we construct a Semi-Lagrangian scheme to solve a numerical solution of the optimal value function that characterizes the risk exposure of the hedger. Special attention is paid to analyzing the truncation error in constructing the numerical scheme and dodging extrapolation. The framework established in this paper generally applies to the hedging problem of equity structures with intermediate payoffs. Numerical studies are conducted to show the effectiveness of the hedging strategy.

3:45 PM - 4:15 PM Title: Local Time and Guaranteed Lifetime Withdrawal Benefit with Step-up Feature Presenter: Chongda Liu, University of Illinois at Urbana– Champaign Abstract: Guaranteed lifetime withdrawal benefit (GLWB) with the step-up feature is among the most popular riders for variable annuity contracts. While there has been pioneering work on the subject matter by Piscopo and Haberman (2011), Huang, Milevsky and Salisbury (2014), etc, most literature on the valuation problem are based on numerical solutions. This paper offers a unique perspective to formulate the valuation problem through the application of the Skorokhod equation. Consequently, we obtain analytical solutions to risk-neutral value of the GLWB rider with roll-up feature in the waiting time and the step-up feature throughout lifetime, which lead to highly efficient algorithms for pricing and dynamic hedging of GLWB riders.

4:15 PM - 4:45 PM Title: Predicting the time of the highest gain for the money makers (in share/stock marked) Presenter: Mian Adnan, Indiana University Bloomington Abstract: Financial turmoil is a fear or a lucrative feature for a latent or a set of latent reasons to the investors or money makers respectively. Besides, financial organizations want to predict the financial turmoil or volatility for implementing its short run or long run derivatives and/or prerequisites as early as possible. Volatility in S & P 500 index Stock Prices signifies the financial turmoil. A step by step approach of quickly identifying the model for the most important latent variable has been inaugurated for demonstrating the capricious behavior of the time series pattern of S&P 500 index strike price-changes over time using the optimum number of predictor(s). The resultant time series model checks the series of sequences of the moving variances of the residuals

to identify which set of few time points contribute the highest variation in the prices. The money makers want to predict these time points.

Friday, August 10, 2018 Session 8E: Risk Measures and Models Time: 3:15 PM – 4:45 PM Location: UCC 60 Chair: Yvonne Chueh, Central Washington University 3:15 PM - 3:45 PM Title: Simulation of systemic events based on random banking networks Presenter: David Hoskins, University of California – Santa Barbara Abstract: We investigate the relationship between systemic risk and the structure of borrowing and lending between banks. We define systemic risk as the event of a large number of banks defaulting. We model a banking system, with capital of banks modeled as stochastic processes. New banks can emerge at random moments, and banks can also default at random times, with contagion effects on other banks. We study properties of such systems: existence and uniqueness, long-term stability, large systems limit. For each set of parameters we run Monte Carlo simulations to estimate the associated default distribution. Finally we perform analysis on this simulated data to explore importance of parameters and network structure. We find that increases in amount of borrowing between banks leads to a decrease in average number of defaults but an increase in further defaults once one bank has defaulted. We also find that a high value for correlation of random shock affecting each bank leads to probabilities of a high number of banks defaulting. 3:45 PM - 4:15 PM Title: Maximum Likelihood Estimation for phase-type aging models Presenter: Boquan Cheng, Western University Abstract: The phase-type aging model is a parametric model used for modelling mortality. Generally, it is hard to fit this type of model due to its flexibility. In this talk, we propose a special class of Coxian phase-type distributions where the absorption (mortality) rates have a simple functional form based on the Box-Cox transformation. Furthermore, we provide a computationally efficient algorithm to calculate likelihood functions. Simulated data and population mortality data are used to fit our proposed model.

4:15 PM - 4:45 PM Title: Evaluation of the Ruin Probability in Ordered Risk Models Presenters: Michael Brown and Daniel Rondon, University of California - Santa Barbara Abstract: A study of numerical methods for computing non-ruin probabilities under a classical risk process is conducted. A Monte Carlo simulation-based method to compute ruin probabilities in the ordered risk model is proposed. A numerical comparison, in terms of accuracy and computing time, between a Monte Carlo-based estimator relying on Appell polynomials and a standard Monte Carlo evaluation is made. After selecting a numerical method, the sensitivity of the ruin probability with respect to the claim sizes distribution and the claim arrival process is studied.

Saturday, August 11, 2018 Session 9A: Actuarial Education II Time: 8:45 AM – 10:15 AM Location: McKellar Room Chair: Jim Trimble, University of Connecticut 8:45 AM - 9:15 AM Title: Open Actuarial Textbooks Project Presenter: Edward W. (Jed) Frees, University of Wisconsin - Madison Abstract: In this talk, I outline a project designed to develop open actuarial textbooks.Many will remember the days before open statistical software such as "R" was available. The availability of free open software has transformed the way that we teach and do research. Will the same be said of textbooks in the future?Currently available authoring tools allow us to produce not only aesthetically pleasing pdf formatted files but also other media including web-based (e.g., html) and EPUB versions (for mobile readers). In particular, web-based versions promote active learning by allowing authors to introduce interactive features that will allow a student to actively explore the content. The talk will provide an overview of the project. Additional background materials are available at https://ewfrees.github.io/ and https://sites.google.com/a/wisc.edu/loss-data-analytics/.

9:15 AM - 10:15 AM Title: Best Practices in Exposing Actuarial Students to Property and Casualty Insurance, Featuring the CAS University Award Winners Presenters: Tamar Gertner, Casualty Actuarial Society; John Zicarelli, Arizona State University; Alisa Walch, University of Texas at Austin Abstract: The CAS honored three universities in 2018 for doing exemplary work preparing students for a career in the property and casualty insurance industry. 2018 honorees include Arizona State University, University of Texas at Austin, and Renmin University of China. These schools were selected for the award based on their efforts in the areas of curriculum, research, industry engagement, and innovation. The goal of the award program is to facilitate the promotion and sharing of ideas within academic communities, and this session will focus on how these schools, in their own words, have been incorporating property and casualty research, content, and experiences for students into their actuarial programs. Prepare to come away from this session with new ideas to add property and casualty research and topics into your program.

Saturday, August 11, 2018 Session 9B: Risk Measures and Dependence Time: 8:45 AM – 10:15 AM Location: UCC 146 Chair: Arnold Shapiro, Penn State University 8:45 AM - 9:15 AM Title: Properties of risk measures inspired from a ruin model with interest Presenter: Ilie Radu Mitric, Universite Laval Abstract: Recent research has established some connetions between ruin theory for the classical Cramer-Lundberg risk model and several risk measures with respect to the stochastic ordering of claim severities. We explore some extensions. For the classical ruin model we investigate some properties of a risk measure derrived from the Laplace transform of the ruin time. Then, for an enhanced model that include the effect of the interest rate, we study a risk measure derrived from the so called expected area in red (expected area of the negative part of a risk process).

9:15 AM - 9:45 AM Title: Introducing dependence between frequency and severity in collective risk model Presenter: Peng Shi, University of Wisconsin-Madison Abstract: In this article, we introduce a regression model for compound distributions that allows for arbitrary dependence between the primary (frequency) and the secondary (severity) variables. Relaxing the independence assumption in standard methods, we employ a parametric copula to accommodate the association between the frequency and severity components. The resulting copula regression framework is flexible enough to nest several commonly used approaches as special cases, including the hurdle model, the selection model, and the two-part model, among others. We further show that the new model can be easily modified to account for incomplete data due to censoring or truncation. Because of the parametric nature, likelihood-based approaches are proposed for estimation, inference, and diagnostics.In the application, we consider the collective risk model for aggregating losses in an insurance system. Using granular claims data in property insurance, we find substantive negative dependency between the number and the size of insurance claims. We demonstrate that ignoring the frequency-severity association could lead to biased decision-making in insurance operations.

9:45 AM - 10:15 AM Title: Estimating Loss Reserves Using Hierarchical Bayesian Gaussian Process Regression with Input Warping Presenter: Nathan Lally, The Hartford Steam Boiler Inspection and Insurance Co. Abstract: In this paper, we visualize the loss reserve runoff triangle as a spatially-organized data set. We apply Gaussian Process (GP) regression with input warping and several covariance functions to estimate future claims. We then compare our results over a range of product lines, including workers’ comp, medical malpractice, and personal auto. Even though the claims development of the lines are very different, the GP method is very flexible and can be applied to each without much customization. We find that our model generally outperforms the classical chain ladder model as well as the recently proposed hierarchical growth curve models of Guszcza 2008 in terms of point-wise predictive accuracy and produces dramatically better estimates of outstanding claims liabilities.

Saturday, August 11, 2018 Session 9C: Statistical Methods Time: 8:45 AM – 10:15 AM Location: UCC 37 Chair: David Stanford, Western University 8:45 AM - 9:15 AM Title: Economic Scenario Generator and Parameter Uncertainty: A Bayesian Framework Presenter: Jean-Francois Begin, Simon Fraser University Abstract: In this presentation, we study parameter uncertainty and its actuarial implications in the context of economic scenario generators. To account for this additional source of uncertainty in a consistent manner, we cast Wilkie's four-factor model into a Bayesian model. The posterior distribution of the model parameters is estimated using Markov chain Monte Carlo methods and is used to perform Bayesian predictions on the future values of the inflation rate, the dividend yield, the dividend index return, and the long- term interest rate. According to US data, parameter uncertainty has a significant impact on the dispersion of the four economic variables of Wilkie's framework. The impact of such parameter uncertainty is then assessed for a portfolio of annuities: the right tail of the loss distribution is significantly heavier when parameters are assumed random and when this uncertainty is estimated in a consistent manner. The risk measures on the loss variable computed with parameter uncertainty are at least 20% larger than their deterministic counterparts.

9:15 AM - 9:45 AM Title: Actuarial Applications of Word Embedding Models Presenter: Gee Lee, Michigan State University Abstract: When data are compiled for empirical analysis, often times a lot of useful information is discarded, because traditional empirical analysis requires numeric descriptor variables. Although textual data contains a lot of information, how to utilize this gold mine of information has been in veil because of technical difficulties. This presentation will demonstrate how empirical analyses can be improved by allowing textual data to be easily incorporated into a standard regression analysis. Using the concept of word similarities, we illustrate how to extract variables from text and incorporate them into a standard regression model. This procedure is applied to the Wisconsin Local Government Property Insurance Fund (LGPIF) data, in order to demonstrate how insurance claims management and risk mitigation procedures can be improved. Word embedding matrices are used to transform insurance claim descriptions into a collection of vectors, and the resulting explanatory variables are used for the analyses. We illustrate three applications. First, we show how the claims classification problem can be solved using textual information. Second, we use a generalized additive model framework to analyze the relationship between risk metrics and the probability of large losses. Third, we illustrate how insurance claim sizes can be predicted using an initial description of the claim. 9:45 AM - 10:15 AM Title: Robust and Efficient Fitting of Severity Models and the Method of Winsorized Moments Presenter: Vytaras Brazauskas, University of Wisconsin- Milwaukee Abstract: In this talk, we will present a new method---the method of Winsorized moments (MWM)---for estimation of the parameters of claim severity models. This method is conceptually similar to the method of trimmed moments (MTM) and thus is robust and computationally efficient. Both approaches yield explicit formulas of parameter estimators for log-location-scale families and their variants, which are commonly used to model claim severity. Large-sample properties of the new estimators are provided and corroborated through simulations. Their performance is also compared to that of MTM and the maximum likelihood estimators (MLE). In addition, the effect of model choice and parameter estimation method on risk pricing is illustrated using actual data

that represent hurricane damages in the United States from 1925 to 1995. In particular, the estimated pure premiums for an insurance layer are computed when the lognormal and log-logistic models are fitted to the data using the MWM, MTM, and MLE methods.

Saturday, August 11, 2018 Session 9D: Insurance Topics Time: 8:45 AM – 10:15 AM Location: UCC 41 Chair: Mario Ghossoub, University of Waterloo 8:45 AM - 9:15 AM Title: Optimal Index Insurance Design Presenter: Chengguo Weng, University of Waterloo Abstract: We study the problem of optimal index insurance design under an expected utility maximization framework. For general utility functions, we formally prove the existence and uniqueness of optimal contract, and develop an effective numerical procedure to calculate the optimal solution. For exponential utility and quadratic utility functions, we obtain analytical expression of the optimal indemnity function. Our results show that the indemnity can be a highly non-linear and even non-monotonic function of the index variable in order to align with the actuarial loss variable so as to achieve the best reduction in basis risk.Our method is illustrated by a numerical example where weather index insurance is designed for protection against the adverse rice yield using temperature and precipitation as the underlying indices. Numerical results show that our optimal index insurance significantly outperforms linear-type index insurance contracts in terms of reducing basis risk. 9:15 AM - 9:45 AM Title: Optimal Insurance under Rank- Dependent Utility and Incentive Compatibility Presenter: Shengchao Zhuang, University of Nebraska Lincoln Abstract: Bernard et al. (2015) study an optimal insurance design problem where an individual’s preference is of the rank-dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their results suffer from the unrealistic assumption that the random loss has no atom, as well as a problem of moral hazard that provides incentives for the insured to falsely report the actual loss. This paper addresses these setbacks by removing the non-atomic assumption, and by exogenously imposing the “incentive compatibility” constraint that both the indemnity function and the insured’s retention function be increasing with respect to the loss. We characterize the optimal solutions via calculus of variations, and then apply the result to obtain explicitly expressed contracts for problems with Yaari’s dual criterion and general RDU. Finally, we use numerical examples to compare the results between ours and that of Bernard et al. (2015). 9:45 AM - 10:15 AM Title: Optimal insurance with background risk: an analysis of general dependence structures Presenting Author: Wei Wei, University of Wisconsin – Milwaukee Abstract: When seeking for insurance, decision makers usually need to take multiple sources of risks into consideration. This raises the problem of how to design optimal insurance policy in the presence of background risk. In the study of this problem, the dependence structure between the insurable risk and background risk plays an important role and also brings the main challenge. In the literature, most studies focus on the the positive dependence and seldom consider other types of dependence structures. In this talk, we shall establish a sufficient and necessary condition to justify the optimality of an insurance strategy under any dependence structure. This results provides a big picture about the structure of an optimal insurance strategy. Then, we partition the dependence structure into three categories, namely, positive dependence, moderate negative dependence, and strong negative dependence; and find out the optimal insurance strategy under each category. Furthermore, we study the optimization problem under several mixed dependence structures. These studies provide insights to ultimately solve the optimal insurance problem under an arbitrary dependence structure.

Saturday, August 11, 2018 Session 9E: Actuarial Modeling II Time: 8:45 AM – 10:15 AM Location: UCC 60 Chair: David Carozza, Université du Québec à Montreal 8:45 AM - 9:15 AM Title: Simulated Minimum Hellinger Distance Estimation for Some Continuous Financial and Actuarial Models Presenter: Claire Bilodeau , Universite Laval Abstract: Minimum Hellinger distance (MHD) estimation is extended to a simulated version with the model density function replaced by a density estimate based on a random sample drawn from the model distribution. The method does not require a closed-form expression for the density function and appears to be suitable for models lacking a closed-form expression for the density, models for which likelihood methods might be difficult to implement. Even though only consistency is shown in this paper and the asymptotic distribution remains an open question, our simulation study suggests that the methods have the potential to generate simulated minimum Hellinger distance (SMHD) estimators with high efficiencies. The method can be used as an alternative to methods based on moments, methods based on empirical characteristic functions, or the use of an expectation-maximization (EM) algorithm. 9:15 AM - 9:45 AM Title: Clustering the events from the earthquake catastrophe modeling catalog Presenter: Baldvin Einarsson, AIR-Worldwide Abstract: Natural catastrophe (CAT) models, which are integral to quantifying the financial risk of an insurance portfolio, rely on stochastically generating a significant number of events in a large catalog of years. Loss computations can be intense, so we investigate methods to cluster the events from a 100,000 year catalog for earthquake peril, thus compressing the catalog size and reducing the loss analysis run time. We describe how certain events are excluded from clustering, such as the most extreme events and events on known fault lines. The methods used for clustering are all deterministic, and include BIRCH, k-means coupled with a deterministic initialization algorithm, along with local outlier factors to identify outliers. This facilitates reproducibility of the results. We analyze losses from the industry exposure database (IED) in Japan, aggregated to two different geographical resolutions; the prefecture level and ku level for two prefectures. The results show that various loss metrics, such as average annual loss (AAL), exceedance probabilities (EP), and tail-value-at-risk (TvaR) are preserved in the compressed catalog. We also demonstrate that physical catalog characteristics, e.g. magnitude distributions, match the original ones.

9:45 AM - 10:15 AM Title: Conventions of quantification and the good use of actuarial models: encouraging critical thinking by humanities Presenter: Christian Walter, Fondation Maison des sciences de l’homme Abstract: The practice of modelling, largely used by actuaries, has been profoundly modified with the emergence of new mathematical techniques mainly derived from academic research in the mathematical finance. These new techniques have hugely contributed to the financialisation of actuarial methods. This financialisation process of the actuarial practices carries new methods of problem analysis, calculation techniques and decision-making principles, well analysed in the actuarial literature (e.g. Day, 2003; IAA, 2008; Whelan, Bowie, Hibbert, 2002). My objective here is to complete the technical actuarial literature with a “humanities-based” approach. I will use the notion of “conventions of quantification” (Chiapello and Walter, 2016) to make clear a possible interest of social sciences for actuaries. Using social sciences methodology, I analyse how quantification conventions influence professional practices. Financialised conventions are replacing

the old reasoning and forms of calculation previously used in actuarial practices. For example, market- consistent valuation based on the risk-neutral pricing method is a financialised valuation. In particular, my aim is to question the notion of the risk-neutral approach and its consequences for insurance and society. How are actuaries reacting to the deployment of this risk-neutral quantification? Secondly, the issue of the actuarial expertise must be rethought after this financial transformation of mathematical models. This is all the more so as actuaries are now called upon to exercise “expert judgment” in complex situations in which there is no history of the relevance of a model to a given situation. The professional expertise expected of actuaries, in particular their expert judgment, constitutes the basis of their trustworthiness. Trustworthy actuaries should be capable of making an accurate diagnosis of risk models, knowing the side effects of the risk models they prescribe, capable of recognising the boundaries of their own capacities to master risk models, capable of seeing if their risk models are up to date. Hence two consequences: on one hand, the importance of understanding the relationship between a mathematical model and its epistemic framework; on the other hand, the need to identify possible dangers arising from the financialisation of epistemic frameworks. To address these issues, an efficient toolbox can be found with history and epistemology of models. The virtue of an historical and epistemological approach to actuarial practices is that of showing both the risks and the consequences of implicitly importing a model from one theoretical context (that of mathematical finance) to another (actuarial modelling). Retracing the history of a model means to assess its epistemological value for the present, thus also opening to the possibility of thinking otherwise and of fostering critical thinking. The paper is organised as follows. I identify three periods, each one associated with conventional calculation systems that may inform investment decisions. Each of these periods begins with the adoption by actuaries of a new “convention” to make decisions: the classical actuarial convention at the end of the 19th century, the mean-variance convention since the 1970s and the market- consistent convention since the 1990s. These conventions are rooted into mathematical finance developments and are associated with different techniques. The arrival of a new convention does not necessarily quash the previous convention, which can continue to be used by actuaries for certain given matters, but it can also redefined some actuaries habits by fragmenting them according to the convention followed, and it can finally also give rise to brand new organised actuarial activities. This example will allows clarifying some important issues of the standard ISAP1 # 2.7.2: “the appropriateness of the assumptions underlying each component of the methodology used.”

Saturday, August 11, 2018 Session 10A: Plenary Session IV Time: 10:30 am – 11:45 am Location: McKellar Room Chair: David Stanford, Western University 10:30 AM – 10:40 AM Invitation to ARC 2019 by Jeff Beckley, Purdue University

10:45 AM – 11:45 AM Keynote Presentation Title: Replacing the Replacement Rate: How Much is ENOUGH Retirement Income? Presenter: Bonnie-Jeanne MacDonald, Ryerson University Abstract: For years, the standard for measuring retirement income adequacy has been the final earnings replacement rate (usually targeted at 70%). Financial planners, actuaries, pension plan advisors, academics and public policy analysts all use this benchmark. It’s the measure that underlies our pension systems, drives the research that determines whether populations are prepared (or not) for retirement and serves as the backbone of retirement planning software. But the question is, does it work? Will 70% of a worker’s final annual employment earnings actually sustain his or her living standards after retirement? This presentation examines whether workers who hit this target can expect to maintain their living standards in retirement and provides an alternative, more accurate basis for assessing retirement income adequacy: the Living Standards Replacement Rate (LSRR). Based on 10 years of research and analysis in industry, academia and government, this presentation answers the often-posed question, "How much is ENOUGH retirement income?" This award-winning work is now being used to foster a clearer understanding of retirement financial security within the financial service industry, government public policy work and by professional associations, promoting more informed decisions and better financial outcomes for Canadians and Americans.