generalised linear modelling for improved...
TRANSCRIPT
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Pricing AdvantageDavid Kirk 2008
Generalised Linear Modelling for improved ratemaking
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How to achievePricing Advantage
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Competition & Market Dynamics
Sharper ratemaking can provide a competitive advantage for increased market share and higher margins
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Rating uncovers hidden risk characteristics
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So that we can group risks and price effectively
Cla
im S
ize
Claim Frequency
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-50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
Current Premium Subsidies
Why we need to rate more accurately
Subsidised Subsidising
Unprofitable Risk being undercut
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Modelling the potential benefitsPolicyholder behaviour and market dynamic model
Needs plenty of assumptions Price sensitivity
Information accessibility
Loyalty
And estimatesDistribution of policyholders by risk
Competitive response
Pricing accuracy
“all models are wrong… but some are useful.”
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Price SensitivityPrice sensitivity If Price Sensitivity is 100%, policyholders always choose cheapest
alternative
If Price Sensitivity is 0%, policyholders ignore price in their decision
Can be estimatedMarket Research and Surveys
Analysis of offer accept and decline statistics
Affects speed of change in market share and equilibrium level
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Information Accessibility Information accessibility If Information Accessibility is 0%, then Price Sensitivity is irrelevant
If Information Accessibility is less than 100%, then the effect of Price Sensitivity is dampened
Can be estimatedMarket Research and Surveys
Can be changed through advertising
Affects speed of change in market share and equilibrium level
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LoyaltyCustomer Loyalty If Loyalty is 100%, no existing clients ever change insurer
If Loyalty is 0%, then at renewal the current insurer has no advantage
Can be estimatedMarket Research and Surveys
Analysis of offer accept and decline statistics
Affects speed of change in market share but not the eventual equilibrium level
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Competitive ResponseNo competitive response assumed for following projectionsNot realistic
Overstates the results
Difficult to quantitatively assess competitive response Prefer to model knowing it’s incorrect
Rather than model something which we don’t understand
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0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 2 3 4 5 6 7 8 9 10
Years in projection
Projected Market Share
Some actual results
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0%
2%
4%
6%
8%
10%
12%
14%
16%
1 2 3 4 5 6 7 8 9 10
Op
erati
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al R
esu
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Years in projection
Projected Profitability (assuming no competitive
reaction)
Some actual results
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Seeing the light
A South African insurer started in 1998 now has over 10% market share, higher than average profitability using advanced ratemaking
Top 20 US insurers all using multivariate techniques
Even more prevalent in UK
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What makes good rates?
A good ratemaking process will generate rates that achieve specific objectives
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Choosing Rating ObjectivesAccuracy
Ease and cost of administration
Flexibility of approach
Statistical efficiency of estimates
Consistency over time
Objectivity and freedom from manipulation
Transparency
Consistent with other corporate objectives
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Correlation, causation and predictive valueCorrelation does not imply causationA vehicle accident or restaurant fire last year does not cause the
accident or fire this year
A prior accident or fire claim is a useful predictor of future claims
Correlation can have predictive value even if there is no causationRating factors versus risk factors
Understanding the cause is preferable, but not required in order to use the factor
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Introduction to statistical ratemaking
Scientific ratemaking doesn’t have to be complex
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Univariate AnalysisConsider one rating factor at a timeAge
Gender
Vehicle Make
Property type
Simple analysis can be performed in a spreadsheet
Can be performed on Loss Ratios
Pure Premiums
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Loss Ratio AnalysisConsider differences in Loss Ratios between different rating
factors or groups
Data requirements Premium and claim amounts for each policy
Premiums for prior periods must be re-rated to be consistent with current rating standards
May require re-underwriting if underwriting approach has changed
Rating factors associated with each policy
New rates are an adjustment to old rates
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Loss Ratio Analysis example
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Pure Premium AnalysisThe Pure Premium is the absolute premium rate applied to the
exposure
Frequency & Severity estimated separately
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Pure Premium Analysis
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Pure Premium example
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Pure Premium AnalysisBased on exposures rather than premiums
Doesn’t require re-rating of past premiums to current on-level premiums
Analysis isn’t affected by special or negotiated rates
Can be used for a new line without an existing basis
Requires a coherent exposure measureUnique or idiosyncratic risks not well suited
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Advanced Scientific Ratemaking Ratemaking
Multivariate, robust, accurate, flexible, understood and competitive ratemaking using GLM
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Revisiting correlation, causation and predictive valueCorrelation does not imply causation
Correlation can have predictive value even if there is no causation
Correlation is a measure of linear relationshipsNot all relationships of interest are linear
Correlation doesn’t guarantee low variance of prediction
Correlation neither sufficient nor necessary to be predictive
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Univariate analysis is flawed
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Comparison of GLM and Univariate Rates
GLM Univariate
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Multiple Regression
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Theoretical and practical problems
Multiple Regression assumes normal distribution of residualsCommon actual distributions for frequency is Poisson and for severity
is Gamma
Multiple Regression can lead to frequencies and severity estimates less than 0
Can still be usefulWidely understood technique
Can even do analysis in a spreadsheet
Problems with Multiple Regression
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GLM: Some evidenceGLM is used widely and successfully in insurance around the
world
Part of ultra-competitive UK non-life industry for many years
Growing quickly in the US since 1990s introductionAs pricing restrictions are reduced, competition has increased
Top 20 insurers all use GLM now
Casualty Actuarial Society heavily involved
Expensive software available, and in demand
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GLM: Basic conceptsGLM is still a form of linear modelling
Generalised to allow for different distributionsAnd technically, we need iterative estimation techniques
But practically this has little effect given current computing power
And making use of transformations of the dependent variable
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GLM: The Link Function
g is known as the Link Function and links the expected value of the dependent variable to a linear combination of risk factors or exposure measures
Can choose any monotonic link function
But natural or canonical links exist for each distribution of the dependent variable
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GLM: The Link Function
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Modelling Claim Frequency with GLM
Canonical Link is Log Link.Scales mean and variance to be constant
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Modelling Claim Severity with GLM
Canonical Link is Inverse Link
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Example Frequency functionVehicle accident damage
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Example Frequency function
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Plot of Frequency FunctionObserved Data
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Possible Model 2Gender
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Possible Model 3Age and Gender
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Possible Model 4Age, Gender, and Interaction
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Selected Model 5Age, Gender, Age-squared + all interaction terms
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Final fitted model 5Age, Gender, Age-squared + all interaction terms
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Plot of Frequency FunctionAge, Gender, Age-squared + all interaction terms
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The role of skill, experience and judgementCritically important in model selection and validation
No time to cover in detail here
Model Selection Forward, Backwards, Hierarchical and All Subsets
Model criteria Likelihood, Deviance, Akaike Information Criterion
Diagnostic testsResidual plots, serial correlation, constant variance
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Combine estimates of frequency and severity into modelled pure premium for each rating group
Make adjustments if necessary Legal minima, maxima
Restrict large changes
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Adjusting rates for riskOnce we have derived pure premiums based on detailed
analysis of multivariate effects on severity and frequency, we need a method to allow for systematic risk
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Problems of variabilityAccepted that greater risk requires greater reward
Not all lines of business are equal in risk to insurer
Diversification is imperfectnon-homogenous claims
systematic estimation error
large claims
correlations and concentrations of risk
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Pricing for variabilityLow reinsurance retentions can reduce these problems
But unless reinsured 100%, some risk remains
Historically, insurers have priced: judgement, heuristics and rules of thumb
proportional to portfolio variance
Current best practice is pricing relative to: Systematic contribution to risk
Economic Capital requirements
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Not just ratemakingSimilar techniques can be used in other business-critical areas of
general insurance, life insurance and banking
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Credit Scoring ModelsCredit Scoring in banking analogous to ratemaking in non-life
insurance Fundamental to business
Source of significant competitive advantage
Generalised Linear ModelsCan perform independent check on current approach
Replace existing methods
Early warning for deteriorating credit
Easier interpretation than discriminant models
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Cross-selling OpportunitiesFinancial Services Groups can increase market share and
profitability through increased cross-selling Typically follow:
a scatter approach; or
time-intensive, inaccurate judgement approach
Little analysis on effectiveness of tactics
GLM can improve: improve hit rate, limit customer annoyance and lower costs
Provide feedback to improve future targeting
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Renewal and Acquisition ModellingApplications of GLM to new sales and renewal pricing
decisions
Interacts with the market dynamics models introduced earlier
Understand what factors lead to renewal probabilities and acceptance of offers for new policies
Optimise pricing: increase margins with limited impact on market share
profitably increase market share
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Renewal and Acquisition Rating FactorsCan use existing rating factors as a staring point
E.g. age, age of vehicle, make and model of vehicle, vehicle use, marital status, vehicle ownership status
But also additional factorsAbsolute size of current premium
Time since policy written / number of times renewed
Competitor’s premiums
Actual vs indicated premium
Level of No Claims Discount / Bonus Malus
Distribution channel
Economic conditions (inflation, interest rates, GDP)
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Renewal and Acquisition Price Sensitivity / ElasticityMost importantly, proposed increase in premium
In original policyholder behaviour model we had to assume a level of price sensitivity
Now we can estimate this, scientifically, for different types of policyholders
Measure what premium can be tolerated with a given probability of cancellation
And differentiate between different types of policyholders
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What aboutNeural Networks?Artificial Neural Networks are mathematical modelsCan be used to build predictive models
Based on many interconnected artificial neurons
Use training algorithms to teach the network how to predict claims
Less widely known and understood than GLMAre in fairly wide use in predictive modelling outside insurance
Black-box limitations
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Making it happenTheory is only useful when it is implemented effectively and
efficiently.That means Systems & Data.
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Steps to Make It Happen1.Commit to investigate advanced ratemaking
2.Select a Champion to drive the project
•Sufficiently senior to ensure progress
3.Assemble project team
•Including marketing, underwriting, actuarial, IT, legal
4.Generate possible rating factor ideas
5.Select or build database to store relevant data
6.Build GLM rating systems and select models
7.Test results in the market
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The Need for SystemsAnalysis of offer accept and decline statistics
Store accurate exposures and claims
Start storing information for future analysisNeed data to assess rating factors
Can’t only store for factors we know are important
Need quick, reliable analysis
Build near-permanent competitive advantage
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Typical analysis requirementsSome large companies will interrogate 200 or 300 possible
variables Large data sets
Robust systems to store data and manage model selection
Need to separate exposures and claims between: Perils
Rating factors (used and possible)
With accurate dates
Database requires robust controls to maintain data integrity and ease of extraction
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Available GLM SoftwareThree primary choices:
1.Purpose-built GLM software for insurance applications
2.Leverage proprietary statistical software
3.Leverage open-source statistical software
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Purpose-built insurance GLM softwareSupports key applications to insurance out of the box
Need to import data in correct format
Expensive licences
Reliant on service provider
But service provider can provide useful, directly relevant support
Requires specialised, mobile skills
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Proprietary statistical softwareRequires more initial effort to access required functionality
Need to import data in correct format
Expensive licences
Reliant on service provider
Service provider can provide generic support
Requires fairly widespread skills
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Open-source statistical softwareRequires more initial effort to access required functionality
Need to import data in correct format
No licence fees
Codebase and algorithms peer reviewed and extensively used in academia and business
Plenty of resources available, but limited paid support
Requires fairly widespread skills
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Common PitfallsEvery technique can be misused.
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People ProblemsFailing to get full buy-in from key stakeholdersOrdinary change management problems
Can develop prototype project
Specific Objectives
Specific Resources
Need vision to recognise long-term imperative
Past success can be an inhibitor to success
Relying too heavily on pre-analysisMultivariate techniques give different results!
-50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
Current Premium Subsidies
Subsidised Subsidising
Unprofitable Risk being undercut
0%
2%
4%
6%
8%
10%
12%
14%
16%
1 2 3 4 5 6 7 8 9 10
Op
erati
on
al R
esu
lt
Years in projection
Projected Profitability (assuming no competitive
reaction)
0.00
0.50
1.00
1.50
2.00
2.50
3.00
MVMSP
MVFSP
MVMGP
MVFGP
MVMRP
MVFRP
MVMSB
MVFSB
MVMGB
MVFGB
MVMRB
MVFRB
MVMSM
MVFSM
MVMGM
MVFGM
MVMRM
MVFRM
Sta
nd
ard
ised
Prem
ium
Rate
s
Comparison of GLM and Univariate Rates
GLM Univariate
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Application Problems 1Not performing sufficient pre-analysis
Using loss ratio analysisVery common mistake, even with large companies
Don’t have standard distributions for loss ratios
Need to adjust data to current rate-level
Difficult to use industry experience to perform sense checks
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Application Problems 2Modelling raw pure premiums for all coverages directly rather
than modelling at the component level Theoretical problems
Awkward, bi-modal distributions
Inferior practical results
Not performing sufficient diagnostic testing on the fitted models while selecting the best model
Treating the predictive model as a black box"
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Not Going Far EnoughRestricting analysis to variables and groupings in the current
rating algorithmConvenient because likely to have data available
Significant advantages to casting net wider
New rating factors
Limiting the use of GLMs to risk models Same technology, skills can be used for other predictive modelling
Renewal modelling can be as valuable as risk models
Extend to credit scoring in affiliated banks?
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AchievingPricing Advantage