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SOA 08 Annual Meeting & Exhibit

October 19-22, 2008

Session 20, Disability Modeling—Designing Effective

and Efficient Models

Moderator

Scott D. Haglund, FSA, MAAA

Authors

Lijia Guo, ASA, MAAA

Trevor C. Howes, FSA, FCIA, MAAA



Lijia Guo, Ph.D., ASA, MAAA

Society of

Actuaries

2008 Annual Meeting, Session 20

October 20, 2008

0Lijia Guo SOA 2008 Annual Meeting

Agenda

IntroductionIntroduction

Generalized Linear Models

Data Mining (DM)

Fully Stochastic Models & Risks Integration

Summary

Lijia Guo SOA 2008 Annual Meeting 1



Why Stochastic

Modeling

Pricing & Underwriting Produce a full distribution of possible outcomes

Confidence levels of held reserves

Consider the volatility of the unpaid claims Individual lines Correlation across the various lines

VAR, CTE

Regulatory and compliance Solvency II IFRS / Fair value accounting Public companies (SEC)

ERM Financial and capital management Operational/strategic excellence


Stochastic Modeling

Generalized Linear Models (GLM)

Generalized Additive Models (GAM)

Data Mining (DM)

Fully Stochastic Models (FSM)

Contingent claim Model (Stochastic Process)

Other Statistics Methods




Agenda

Introduction

Generalized Linear ModelsGeneralized Linear Models

Data Mining (DM)


Summary


Stochastic Models

‐ GLM

iμ

iii

i

j

j jiii

V Y Var

X gY E

ω μ φ

ξ β μ

/)(][

)(][ ,

1

=

+== ∑−

•For each observation i , from distribution with mean

•Y

has

distribution

from

the

exponential

family•g – is called the link function



Stochastic Models ‐ GLM

Y

1

The identity link: g(Y) = Y

The log link: g(Y) = ln(Y)

The inverse link: g(Y) =

The logit link: g(Y) = )1

ln(Y

Y

−

Stochastic Models

‐ GLM

22

22

)(,)(,

)(,)(,1

)(,1)(,

μ φ

μ φ

σ σ φ

k Y Var x xV k

Y Var x xV

Y Var xV

===

===

===

iii V Y Var ω φ /)(][ =

For Normal:

For Poisson:

For

Gamma:



Stochastic Models ‐ GLM

⎟ ⎠

⎞⎜⎝

⎛

− x

x

1ln

φ

2 x

ω

ξ

Y Claim

Frequency Claim #

Average

Claim

Amount

Prob./Lapse

g lnx lnx lnx

Error Poisson Poisson Gamma Binomial

1 1 Estimated 1

V(x) x x x(1‐x)

Exposure 1 # claims 1

0 ln(exposure) 0 0

Stochastic Models

– GLM

Applications



Stochastic Models – GLM Applications

What to do with continuous variables? – Age, Claim Size…

Stochastic Models

‐ GAM

•GLMs are special case of GAMs

•Example

LN(E[PP]) = + f1(age) + f2(gender) +f3(Income) +f4(marital)

•The functions f1,f2,f3,f4 can be anything

‐GLM ‐ Categorical, polynomial, transforms

‐Non‐parametric functional smoothers

‐

Decision

trees

•Balance degrees of freedom, amount of data, and

functional form better




Stochastic Models ‐ GAM

• Error Criteria

∑ {Yi – g(ti) } ² + λ ∫ { g” (t)} ² dt

‐ λ is smoothing parameter

• Applications – P&C

• Reference:

‐ Nonparametric Regression and Generalized Linear Models, Green& Silverman


Agenda

Introduction


Data MiningData Mining


Summary





Stochastic Models

– Data

Mining

An information discovery process.

Knowing your goals Identifying responsive potential customers

Identifying existing customers that more likely to terminate

Identifying low risk purchaser

Identifying the factors that cause large claims

Indentifying interactions among risk factors

Choosing the right methods

Understanding the

limitations

Validation and testing

Make crucial business decisions


Data Mining ‐ Data

Identifying Data

Internal Sources Demographic data

Transactional data

Survey data

External Sources Databases

Survey Data

Competitor

Preparing Data

Transforming Data




Introduction – DM Process

Stochastic Models

– Data

Mining

Decision Trees

Logistic regression

Neural Networks

Fuzzy Logics

Genetic Algorithms

Clustering

Associated discovery

Sequence Discovery

Bayesian analysis

Visualization

Hybrid

Algorithms

• Problems with standard algorithms

• Advanced algorithms

• Discovery-driven approaches

• Mixture of algorithms




What is the best method for you?

Model Assessment

Goodness‐of ‐ fit

Prediction accuracy

Sensitivity and Specificity

ROC curve

Model diagnostics

Pearson Residuals

Deviance Residuals

Hat

Matrix

Diagonal


Model Validation

Cross validation

Avoid misleading

Improve the accuracy

Bootstrap validation

More robust solutions

Confidence measure

Sliding Window validation – for time‐series data

Non‐stationary

Slow‐varying



20

DM in Variable Selection

Improving model accuracy and efficiency

Reducing model complexity/over fitting

Problem

‐‐ Given {Y,X} where

Find F, such that

Find and F*, such that, Z X ⊂( )F X Y ≈

*( )F X Y ≈

1 2{ , ,... } N

X x x x=


Case Study ‐ DM in Underwriting

Data: Group Health with over 100 input variables

Goal: Practical guide for underwriters to use for rates

adjustments

Principle Components Analysis applied

Regression Tree

Final model uses about 10% of the original variables

Improved

profitability

by

50%




Regression Tree Example

Profit=6.5%+0.8% , if AS > 421

-0.5% , otherwise

+1.2% , if maleyoung than 30

-1.1% , otherwise

Two Predictor Dependence For

PROFIT_MARGIN

-0.10

-0.05

0.00

0.05

5000 10000 15000 20000 25000

P a r t i a l D e p e n d e n c e

AVG_SALARY

Two V ariable Dependen ce f or PROFIT_MARGIN; Slice SIZE = 0.99999999

PROFIT_MARGIN

-0.05

0.00

0.05

5000 10000 15000 20000 25000

P a r t i a l D e p e n d e n c e

AVG_SALA RY

Two Variable Dependence for PROFIT_MARGIN; Slice SIZE = 1.02702701

PROFIT_MARGIN


Case Study

‐ Stats

and

Variable

Importance

Input Additive Multiplicative Importance

Variable 1 0.2679 0.2690 100.00

Variable 2 0.2779 0.3203 75.23

Variable 3 0.1456 0.1771 54.65

…

Variable 9 0.1129 0.1148 23.37

Pair Variables Additive Multiplicative

Variable 1 & Variable 2 0.3714 0.3847


…




Desirable Features of a Data Mining

Method Any nonlinear relationship can be approximated

A method that works when the form of the nonlinearity is

unknown

The effect of interactions can be easily determined and

incorporated into the model

The method generalizes well on out‐of sample data


DM Applications in Insurance

Underwriting

Pricing/Rate Making

Claim Scoring

Risk Management

Policy Level Analysis

Cluster Analysis

Variable Selection

Effect

of

Plan

design

on

utilization

and

distributions

Trends and Projections



Agenda

Introduction


Data Mining

Fully Stochastic Models & Risks IntegrationFully Stochastic Models & Risks Integration

Summary


Fully Stochastic Model (FSM)

Risk Scenarios

Economic scenarios

Underwriting risk scenarios

Policyholder behavior

Integrating Risks and Correlations

At Product

level

At Enterprise level

Model Efficiency and Applications




Scenarios

scenario simulation

historical filtered historical Monte Carlo

simulation simulation simulation

volatility correlation

scaling scaling

EWMA GARCH


Case Study

‐ Insurance

Package

Age of insured: 60

Unreduced death benefit 500,000

Deferred annuity

Monthly LTC benefit: min(10,000I(t), %AV), where

I(t) – indexed to the inflation

%AV varies depending on the states of care (ADLs)

Death benefit for disabled: %AV

Maximum LTC benefit: 200,000

Waiting period:

2 years




Stochastic Modeling Insurance

Package

Risk Measure in

Credit Risk

Market Risk

Insurance RiskInsurance Risk

Contingency risks

Catastrophe (Influenza

Pandemic)

Business continuity

Claims

Liquidity

Reinsurance

Risk based value Pricing Underwriting

Reserving

Mortality Risk

General population

Disabled lives

Morbidity Risk

Lapse

Interest risks

Underwriting (anti selection)

Embedded Options

Risks Interaction/correlation Claim reserve


Modeling Insurance Package

‐ contract premium payable at BOY

‐ Discount function

n ‐ Term/length of the contract

APV of the policy premium is

Note the correlations of risks

)()()()()(Pr LTCB APV WB APV DA APV DB APV emiums APV +++=

T v

k P

)'1)('1)('1())(Pr( )()()()( i

xk

w

xk

d

xk xk qqqt xT p −−−=>=τ



LTC Combo ‐ Stochastic Interest Rate

The discount

factor

for

the

cash

flows

at

the

EOY

t is

Where

is the interest rate prevailing in year t:

Example

)1()1)(1(

1

21 t

t r r r

v+++

=L

t r

dzdt r mqdr t t σ +−= )(

004.,0601.,015. === σ mq

LTC Combo ‐ Stochastic Lapse Rate

The lapse rate in year t is

Where

is US 1‐ year T‐bill rate in year t.

Example.

22.,82. 21 == β β

t r

)1,0(,12

)(

11

)( N r qq t t t

w

t

w

t ≈++= −− ε ε β β



LTC Combo ‐ Stochastic Mortality Rate

Mortality Risk: Uncertainty

in

future

mortality

rates

including

increases

and

decreases in mortality rates

Lee‐Carter Model

Cairns‐Blake‐Dowd Model

Longevity Risk: Uncertainty in the long‐term trend in mortality rates.

Normally taken to mean the risk that survival rates are higher than

anticipated.

Short ‐Term, Catastrophic Risk: Risk that over short periods of time, mortality

rates are much higher (or lower) than would normally be experienced. (e.g.,

influenza

pandemic

of

1918).

Stochastic Morbidity Models

‐ LTC benefit paid at different state j of disability, j =1, 2, 3.

‐ Transition probability from State i at time z to State j at time t:

),(

1

ji

k b +

( )∑ ∑=

+

=+ +++=

n

k

xk

k

j

ji

ji

k pvk xk xPb LTCB APV 1

)(13

1

,

),(

1 )1,()( τ



Stochastic Morbidity Models

is the

force

of

transition

from

state

i to

State

j at

time t.

State Transitions in LTC insurance – state of care:

)(, t jiλ

Risk Scenarios

scenario simulation

historical filtered historical Monte Carlo

simulation simulation simulation

volatility correlation

scaling scaling

EWMA GARCH

Monte Carlo (single and multi‐step)

Historical

Stress scenarios, sensitivity shocks

Additive and multiplicative shocks to any risk factor or risk factor node

Principle component analysis, factor reduction, risk‐factor clustering




Scenario s

Interest Rate

Spread

Mortality

MobidityTotal EC

• Multiple individual scenario sets by risk types• Asset and liabilities cash flows are modeled with the 4 scenario sets

• EC calculated based on individual distribution

• Total EC calculated based on the aggregation


Integrating Product Risk/Return

39

0

5

10

15

20

25

Yr 1 2 3 4 5 6

0

5

10

15

20

25

30

35

Yr 1 2 3 4 5 6 7

0

5

10

15

20

25

Yr 1 2 3 4 5 6

-10

-5

0

5

10

15

20

25

30

Yr 1 2 3 4 5 6 7

Time

Enterprise Economic Profit

Product 1 Product 2 Product 3 Product 4

Lijia Guo SOA 2008 Annual Meeting



Effect of Risk Aggregation


Summary Stochastic Modeling provides insight into both A&L

uncertainty

Stochastic models are more complex than traditional models but this makes actuarial analysis and judgment even more

important

Regulatory focus on risk management and disclosure is increasing demand

Optimal Risk Adjusted Return ‐ increase enterprise economic

profit

Q&A




References

England, P and Verrall, R (1999). “Analytic and Bootstrap Estimates

of Prediction Errors in Claims Reserving,” Insurance: Mathematics

and Economics

Guo, L (2001). “Dynamic Method for the Valuation of Fair Value

Insurance Liabilities”, Casualty Actuarial Society, www.casact.org

Guo, L (2003), “ Applying Data Mining Techniques in

Property/Casualty Insurance”, Casualty Actuarial Society ,

www.casact.org

Guo, L (2003), “Data Mining in Insurance Seminar”, Society of

Actuaries, www.soa.org

Guo, L (2007), “Stochastic Modeling in Health Benefits”, Society of

Actuaries, www.soa.org




Disability Modeling:Designing Effective and

Efficient Models

Trevor Howes, FCIA, FSA, MAAA

SOA Annual Meeting – OrlandoSession 20

October 20, 2008

Session 20 PD - Trevor Howes 2

Agenda

• Modeling demands

• Model Efficiency Work Group

• Mathematical and modeltechniques

• Hardware Technology

• Software Technology




Pending Issues ImpactingDisability Models

• Principle-based Approach to reservesand RBC capital – Robust, seriatim deterministic reserve

using gross premium method

– Unlocked assumptions appropriate tobusiness and driven by experience

– Stochastic Reserves and Capital

– Single model for both purposes ?


Pending Issues ImpactingDisability Models

• IFRS (Europe, Canada, Asia, SEC, US?)

• ERM and Economic Capital(Management, Ratings agencies,Parent Corporations)

• Capital Assessment (Solvency II,proposed Canadian MCCSR)

• NAIC has adopted a SolvencyModernization Work Plan (June, 2008)

• Will NAIC adopt IFRS before PBA?




Common threads

• Realistic, probabilistic, risk based focus

• Blend of deterministic and stochastic

• 1000’s or 10’s of 1000’s of scenarios

• Risk of higher volatility of results

• Need for reliability and robustness

• Increased scrutiny of actuary’s judgment and quality of models


Implications on Modeling

• Models must become more effective,more efficient AND … – More granular and policy/plan specific

– More precise for all material risks

– More adaptable to multiple purposes

– More flexible to respond to changes

– More easily documented and audited




Implications on Modeling

• Actuaries must become more effectiveand efficient at modeling

– Need more time for interpretationand analysis of model results

– Spend less time

• building business models

• entering and verifying assumptions

• testing and validating• documenting


Model Efficiency Work Group

• MEWG is a subgroup of the AAA SVL2Committee created in 2007

• Mandate to examine ways to make thecomplex modeling required under PBAmore manageable

• Techniques being examined could

apply generally to all modelingincluding disability




Modeling EfficiencyBibliography

• Actuarial Modeling Techniques

– Scenario design and selection

– Mathematical or model design

– Model data building

• Technology Solutions

– Hardware design

– Software design

• Website link:http://www.actuary.org/risk/pdf/bibliography.pdf


Modeling EfficiencyFor Disability

• Scenario design and selection – stochastic analysis of economic risks

– e.g. PBA and Economic Capital

• Are these relevant or practical forDisability models? – DI has long term interest rate risks

– ALM analysis is useful

– Useful to link dynamic policyholderbehavior to economic scenarios





• Scenario testing requires detailedmodels reflecting realistic cash flows

• Full multi-state model vs. claims costs

– Economic risks impacted by claim runoff

– Termination rates may vary by scenario

– Required to properly understand thebusiness

• Magnifies need for model efficiency



• Mathematical or model design

– Closed form solutions to optionpricing

– Low discrepancy sequences (Quasi-Monte Carlo) vs. full Monte Carlo

– Replicating portfolios

– Predictive models

– Low relevance to Disability models





• Model data building techniques

– Most common solution to runtimeand technology constraints

– Build compressed model using

• Grouped data at selected model points

• Representative plans and risk classes

–

Critical area for Disability models dueto runtimes and data heterogeneity



• Drawbacks of compressing in forcedisability insurance data – Low compression ratios

– Result distortion (model error)

• Especially if risk class substitution

– High effort to create and validate

– Complicates multiple uses of model

• Preferable to use full seriatim ordynamic option to build and selectcompressed version as needed





• Building compressed models – New techniques (Cluster Analysis)

– Adjust compression ratio by blockaccording to sensitivity/significance

– Calibrate and test according to purpose

– Generate both full seriatim andcompressed models for comparison testing,validation, adjusting compression

– Automate compression if possible as partof data extract load & transformation


Technology –hardware solutions?

• For Stochastic analysis, may needfurther 100 to 1000X improvementwhile also meeting requirements for

– Reasonable total cost (hardware, software,IT infrastructure and support)

– Increased reliability, auditability, control

– Increased actuarial productivity and value

• Will technology enable efficientdisability models in foreseeable future?




Technology performance review

• Technology has delivered incrediblyconsistent performance improvements

• For example, over past 10 years, youcould purchase desktop PCs based on:

– 1998 (Pentium II, 400 MHz)

– 2003 (Pentium 4, 2.53 GHz)

– 2008 (Core 2 Quad, 2.66 GHz)


PC Performance1998 - 2008

59.2.017Core2 Quad

2.66GHz

2008

5.8.172Pent 42.53GHz

2003

1.01.000Pent II400MHz

1998

BenchmarkSpeed

BenchmarkTime

Processor Year

Estimates based on seriatim actuarial projection model




PC Performance per $11998 - 2008

133.2$2000Core2 Quad2.66GHz

2008

12.5$2100Pent 42.53GHz

2003

1.0$4500Pent II400MHz

1998

Benchmark Value

ApproxCost

Processor Year


Historical TechnologyImprovements

• Miniaturization has enabled

– higher transistor counts

– faster response

– increased clock speeds

– more instructions per second

– faster buses

• Reduced voltages to manage heat

• Faster and denser memory and drives




Future Innovations

• New materials (hafnium oxide)

• Deep UV optical lithography

• Nanotechnology (molecular level)

• Helium supercooled transistors

• Terahertz transistor

• Trigate transistors (3-d)

• Biocomputing & neural networks

• Quantum computing


Current Technology Trends

• Increased parallelism in processors

– Multiple instructions executed at once

• Multiple processor cores on one chip

– Faster than multiprocessors

– Shorter distances

– Shared bus and cache

– Interface at higher clock speeds

• Intel plans chips with 100+ cores




Personal Grids?

• Personal Cluster “deskside” server

– 340 Gigaflops of computing power

– 8 quad-core processors (32 cores)

– 1 Terabyte disk storage

– Regular 120V wall plug

– Windows CCS O/S installed

– Cost: under $20,000


Parallelism

• Parallelism requires multithreading

• Automatic benefit from OS tasks

• However significant benefit requiresspecific application design changes

– Identify separable non-linear tasks

– Manage thread synchronization

– Data sharing and management




Parallelism and DistributedProcessing

• Distributed Processing requires

– Allocating processing steps to helpers

– Distributing work by Cells, seriatim policies,testing targets (scenarios)

– Monitoring task completion or failure

– Consolidation of results from helpers

– Specific application support


Parallelism and Grids

• In “Grid Computing” as typically used

– Focus on capturing spare capacity formany applications over large network

– Enterprise Grid Managers are notapplication specific or knowledgeable

– May require inserting additional code

– Software license and IT support per node

– 1000+ processors may achieve runtimesbut costly, inefficient, unreliable




The Evolution of Grids

• Trend now to greater use of dedicatedserver farms and/or computer clusters

– Tightly coupled for efficiency

– Easy software installation

– Cost effective O/S and IT support

• Microsoft CCS 2003 & HPC Server 2008 enablessharing grid and scheduling

– Robust and audit friendly – Highly scalable to large farms


Technology Solution –Hardware?

• Will technology enable efficient but complexdisability models in foreseeable future? – Not enough for large stochastic applications yet

– Quite enough now for seriatim, first principles,multi-state models, selected scenarios

• Model efficiency must also consider humancosts of maintenance, control and analysis

• One actuary’s salary plus overhead = cost offarm of 250 + cores?

• Technology can make actuary moreproductive depending on application software




Technology Solution –Software

• Detailed, first principles, multi-statemodel

– Optional claims cost approach

– Enable selective adjustment of eachcomponent of claims cost andunderstanding impact

– Support compound assumptions

– Facilitates experience analysis



• Full seriatim business model for bothvaluation and projection

– Optional selective compression

– Avoid reconciliation and validation

– Enable targeted adjustment of

assumptions at granular level – Supports experience analysis, source

of earnings, reserve movement





• Multiple purpose, multiple basisprojection capabilities

– Avoid reconciliation and validation

– Ease of testing “what if” scenarios,reporting impact of changes

– Both deterministic and stochastic(?)

– Staff productivity with one platformto learn and maintain



• Store assumptions in objects separatefrom model framework, logic and code

– Promote control of code changes,stability, ease of validation, audit

– Facilitate assumption query,documentation, change

– Balance of control vs. flexibility

– Separation of duties; use of skills





• Integrated automated model building – Load of source data and transformation to

feed model (avoid relying on IT dep’t)

– Compress? (if necessary)

– Define and apply rules

• to assign business to “supercells”

• to attach/update assumptions insupercells or at seriatim level

(to reduce numbers of supercells) – Enable auditable start to end batch process


Efficient andEffective Models

• Avoid over simplification of models

– Seriatim, first principles, flexible

• MEWG is studying model efficiencytechniques

• Hardware technology will help

• Software design is critical to userproductivity with models

2008 orlando annual 20

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