Predictive Modeling for Disability Pricing May 13, 2009 Claim Analytics Inc. Barry Senensky FSA FCIA MAAA Jonathan Polon FSA

About Claim Analytics Introduction to Predictive Modeling Disability Pricing Discussion Agenda

About 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 Life o ING Employee Benefits o Lincoln Financial o Mutual of Omaha o Principal Financial o Sun Life Canada o Sun Life US o UNUM Several new product initiatives About Us (Cont’d)

Introduction to Predictive Modeling

Computer Performance MeasureIBM 7094 c Laptop c Change Processor Speed (MIPS).253,00012,000-fold increase Main Memory 144 KB4,000,000 KB28,000-fold increase Approx. Cost ($2008) $11,000,000$2,0005,500-fold decrease

What is a Predictive Model 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 Models 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 Tools 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 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 Approach

Quotes for Claim Analytics employee LTD benefits Uncertainty in Current Rates InsurerRate per $100 Manulife0.539 Great West Life1.110 Empire Life1.850 Sun Life1.986 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 Approach

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 Highlights

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 Requirements

Apply predictive modeling to: Predict claim incidence rates Predict claim severity, conditional upon claim being made for each member of census data The 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 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 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 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 Models

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) = e x μ i = g -1 ( Β 1 x i1 + …+ Β p x ip ) = exp(Β 1 x i1 ) * … * exp(Β p x ip ) GLM 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 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 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 Benefits

Discussion