Predictive ModelingPredictive Modelingforfor

Disability Pricing Disability Pricing

May 13, 2009May 13, 2009

Claim Analytics Inc.Barry Senensky FSA FCIA MAAAJonathan Polon FSAwww.claimanalytics.com

• About Claim Analytics

• Introduction to Predictive Modeling

• Disability Pricing

• Discussion

AgendaAgenda

About UsAbout Us• Founded in 2001 by two actuaries

• Objective: Apply predictive modeling technology to insurance questions

• Current Disability Products• Claim scoring• Claim reserving• Pricing• Benchmarking

• Clients in Canada and U.S.o Blue Cross Lifeo ING Employee Benefitso Lincoln Financialo Mutual of Omahao Principal Financialo Sun Life Canadao Sun Life US o UNUM

• Several new product initiatives

About Us (Cont’d)About Us (Cont’d)

Introduction to Introduction to Predictive ModelingPredictive Modeling

Computer Performance

Measure IBM 7094

c. 1967

Laptop

c. 2008

Change

Processor Speed (MIPS)

.25 3,000 12,000-fold increase

Main Memory

144 KB 4,000,000 KB 28,000-fold increase

Approx. Cost ($2008)

$11,000,000 $2,000 5,500-fold decrease

What is a Predictive What is a Predictive ModelModel

• A Predictive Model is a model which is created or chosen to try to best predict the probability of an outcome

• Have been around for 40+ years

• Harnesses power of modern computers to find hidden patterns in data

• Used extensively in industry

• Many possible uses in insurance:

About Predictive About Predictive ModelsModels

May be parametric…

• apply numerical methods to optimize parameters

• E.g., gradient descent, competitive learning

Or non-parametric

• often have a decision tree form

• typically optimized using exhaustive search

Predictive Modeling Predictive Modeling ToolsTools

Some common techniques

• Generalized linear models

• Neural networks

• Genetic algorithms

• Random forests

• Stochastic gradient boosted trees

• Support vector machines

Why aren’t Actuaries building modern predictive models?

• Life Insurance Industry is conservative and slow to change

• Not a traditional actuarial tool• The times are changing!

– Especially P&C Actuaries• Its only a matter of time!

– It just makes too much sense! – Innumerable applications to help solve

insurance problems

Disability PricingDisability Pricing

• Traditional actuarial methods focus on one, maybe two risk factors at a time

• Solve for one factor, then move to the next

• Unable to account for correlations and interactions between rating variables

• Example: region and industry may be highly correlated and may interact

• Lots of uncertainty in rates

Current Industry Current Industry ApproachApproach

Quotes for Claim Analytics employee LTD benefits

Uncertainty in Current Uncertainty in Current RatesRates

Insurer Rate per $100

Manulife 0.539

Great West Life 1.110

Empire Life 1.850

Sun Life 1.986

• No consistency between insurers

• Does anyone have confidence in their rates?

• Ideally suited to multivariate analysis

Adjust for correlations between variables

Facilitate analysis of interaction effects

Uncover and quantify complex relationships between risk factors and claim experience

Maintain wholeness of data

• Improved accuracy vs traditional methods

• Greater confidence in rates

Predictive Modeling Predictive Modeling ApproachApproach

• Identified a key rating variable that was not priced for in current rates

• Identified and quantified two-way interaction effects between rating variables

• Better quantification of all effects

• Significant improvements compared to existing rates

Recent Project Recent Project HighlightsHighlights

Exposure data:• Census: age, gender, salary

• Plan features: EP, ben%, benefit period, etc

• Group info: SIC, region, size, etc

Claim data:• Policy #: link to plan features and group

info

• Claimant info: age, gender, salary, benefit

• Cost estimate: PV benefits paid plus reserve

Data RequirementsData Requirements

Apply predictive modeling to:

• Predict claim incidence rates• Predict claim severity, conditional upon

claim being made

for each member of census data

The ObjectiveThe Objective

• Flexible, client-defined

• Can be the same as current

• Most common structure is base rates and multiplicative loadings

• Iterative process:• Test multiple structures• Test several rating variables

Rate StructureRate Structure

• Base rates are typically a function of: age, gender, EP and max benefit period

• In low dimensions, with sufficient data, traditional graduation approach works well

• Or, predictive modeling can be used if data is sparse or heterogeneous

Base Rate ApproachBase Rate Approach

• Generalized linear models (GLM) can be used to optimize loading factors

• Accurate, yet efficient can test several combinations of rating factors

• Significant and insignificant rating factors are identified

• Interactions between rating factors can be quantified

Multiplicative LoadingsMultiplicative Loadings

• Predictive modeling technique

• Industry standard for P&C insurance

• Generalization of classical linear regression

• Computationally efficient

• Performs very well for multiplicative models

Generalized Linear Generalized Linear ModelsModels

• Similar to linear regression except that effects are additive on a transformed scale

• Transformation occurs through a link function, g(x)

• Log-link function results in multiplicative effects: g(x) = ln(x) g-1(x) = ex

μi = g-1(Β1xi1 + …+ Βpxip) = exp(Β1xi1) * … * exp(Βpxip)

GLM At A GlanceGLM At A Glance

• Predictive modeling is a decision support tool

• Pure factors can be manually adjusted:• Marketplace pressures• Strategic considerations

• Cost of adjustments can be quantified

The Final Rate ManualThe Final Rate Manual

Predictive modeling facilitates better decisions

• Identify rating variables that the market misprices

Where market overprices, can choose to be aggressive or to keep excess profits

Where market underprices, can choose to avoid unprofitable business or at least know the cost of writing

• Better business mix

• Greater confidence in rates supports decisions as to when and how much to discount

A Marketplace AdvantageA Marketplace Advantage

• Improved accuracy and confidence

• Accurately account for correlations and interactions between rating variables

• Facilitates analysis of new rating variables

• General rate structure can remain the same

• Maintains flexibility in final rates

Predictive Modeling Predictive Modeling BenefitsBenefits

Discussion Discussion