session 76 - how to use predictive modeling to better
TRANSCRIPT
76 - How to Use Predictive Modeling to Better Manage Your Life Insurance Inforce
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Valuation Actuary Symposium
Ben JohnsonSession 76: How to Use Predictive Modeling to Better Manage Your Life Insurance InforceAugust 27, 2019
Agenda
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• Overview of using PA in assumption setting• Machine learning and linear regression
• Overview of case studies and data used• 10 year level term products
• Predicting lapses using Poisson regression and mortality using Logistic regression
• Variable ranking and selection• Feature engineering• Using offsets in linear models• Validating models
Overview of PA in assumption setting
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DIFFICULTY
VALU
E
Descriptive Analytics
What happened?
Diagnostic Analytics
Why did it happen? Predictive
Analytics
What will happen? Prescriptive
Analytics
How can we make it happen?
Source: Gartner (March 2012)
Purpose of Predictive Analytics
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Machine Learning Algorithms
• Pros:• Less restrictive so able to more accurately capture
trends in data• Can require less domain expertise to implement
• Cons:• Non-parametric models can be more difficult to
interpret and use for inference• Prone to overfitting the training data• If used in projections, actual ML modeling object would
need to be embedded in your projection system
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Linear Regression
• Pros:• Closed form model is easy to
implement• Easily interpretable model
coefficients
• Cons:• Requires additional feature
engineering to approximate non-linear trends
• More restrictive, which may sacrifice accuracy
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Case Study Data
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Source of case study data
• MIMSA III Industry dataset • Filtered to 10-year level term life insurance products• Contains combined experience from 28 different
companies
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Note: Large companies were downsampled
Modeling data sets
• In order to demonstrate two different modeling techniques, data was transformed differently for each case study
• Lapse case study:• Aggregated count data• Used for Poisson regression
• Mortality case study:• Seriatim time series data• Used for Logistic regression
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Lapse case study
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Identifying key variables
• Domain knowledge + algorithmic approach• GBM
• Good for picking up nonlinear relationships in data
• Random forest• Similar to GBM but less computationally demanding
• GLM w/ regularization• Regularized effects can be compared apples-to-apples
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Variable DetailsAttained age Age at last birthdayCalendar year In which policy year beganDuration Years since policy issuedFace amount Measured at issuePremium collection Credit card, Direct billing, Other/UnknownPremium increase Cumulative premium increase ratioRisk class Smoker/Nonsmoker preferred classesSex Female, Male, Unisex/Unknown
List of variables considered
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GBM variable importance
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GBM informs feature engineering
• It is not straightforward to extract relationships from a GBM due to non-parametric form
• Partial dependence plots give graphical representation
• Practically limited to univariate and bivariate views
• Non-linearity can be approximated using piece-wise linear effects
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GBM partial dependence – Duration
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Fitting Poisson regression model
• Model form• log𝑌𝑌 = β0 + β1x1 + ⋯+ β𝑛𝑛x𝑛𝑛
• Predicts the number of lapses for a given set of x• In reality, our model needs to predict on datasets of
various sizes• Predicting lapse rates would be more appropriate
• Luckily, our Poisson regression model can predict rates by utilizing an “offset”
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Poisson offset term
log𝑌𝑌 = β0 + β1x1 + ⋯+ β𝑛𝑛x𝑛𝑛 + log𝐸𝐸
→ 𝑌𝑌 = 𝑒𝑒β0+β1x1+⋯+β𝑛𝑛x𝑛𝑛 ∗ 𝐸𝐸
→ 𝑌𝑌𝐸𝐸
= 𝑒𝑒β0 ∗ 𝑒𝑒β1x1 ∗ ⋯ ∗ 𝑒𝑒β𝑛𝑛x𝑛𝑛
So… coefficients correspond to multiplicative factors on the lapse rate
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Lapse model summaryEstimate Std. Error P-Value Sig
Intercept 3.365 0.055 <0.001 ***Duration -0.503 0.004 <0.001 ***TermPhaseIN -6.861 0.046 <0.001 ***TermPhaseOUT -5.648 0.057 <0.001 ***Premium increase 0.380 0.008 <0.001 ***Premium increase in excess of 4 -0.310 0.008 <0.001 ***Premium increase NA indicator 1.038 0.021 <0.001 ***Premium collection – Credit -0.710 0.004 <0.001 ***Premium collection – Other/Unknown -0.166 0.002 <0.001 ***Attained age -0.003 0.000 <0.001 ***Duration:TermPhaseIN 0.424 0.005 <0.001 ***Duration:TermPhaseOUT 0.434 0.005 <0.001 ***
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Relative risk ratios
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• β𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = −0.71, β𝑜𝑜𝑐𝑐𝑜𝑐𝑐𝑐𝑐 = −0.166, β𝑏𝑏𝑐𝑐𝑏𝑏𝑏𝑏 = 0• π𝑏𝑏 denotes the probability of lapse for group 𝑙𝑙
→ π𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐π𝑏𝑏𝑐𝑐𝑏𝑏𝑏𝑏
= 𝑐𝑐β𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐β𝑏𝑏𝑐𝑐𝑏𝑏𝑏𝑏
= 𝑒𝑒−0.71 ≈ 49%
→ π𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐π𝑜𝑜𝑐𝑐𝑜𝑐𝑐𝑐𝑐
= 𝑐𝑐−0.71
𝑐𝑐−0.166 ≈ 58%
→ π𝑜𝑜𝑐𝑐𝑜𝑐𝑐𝑐𝑐π𝑏𝑏𝑐𝑐𝑏𝑏𝑏𝑏
= 𝑒𝑒−0.166 ≈ 85%
Model validation – Duration
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Model validation – Premium increase
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Mortality case study
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Fitting Logistic regression model
• Model form• log π
1−π = β0 + β1x1 + ⋯+ β𝑛𝑛x𝑛𝑛• Predicts the probability of death for a given set of x• But standard mortality tables already work well??• Yes, I agree! So let’s instead fit a model which fine-
tunes those predictions to our data• We’ll use an offset that is based on the 2015 VBT
(select and ultimate)
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Logistic offset term
log π1−π = β0 + β1x1 + ⋯+ β𝑛𝑛x𝑛𝑛 + log 𝑝𝑝
1−𝑝𝑝
→ log π1−π− log 𝑝𝑝
1−𝑝𝑝= β0 + β1x1 + ⋯+ β𝑛𝑛x𝑛𝑛
→π
1−π𝑝𝑝
1−𝑝𝑝= 𝑒𝑒β0+β1x1+⋯+β𝑛𝑛x𝑛𝑛
• Model predicts deviations from VBT log-odds• Coefficients correspond to multiplicative factors on the
associated odds ratio
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Mortality model summary
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Estimate Std. Error P-Value SigIntercept -0.027 0.090 0.761Duration -0.008 0.003 0.015*TermPhaseOUT 0.202 0.036 0.000***Premium increase 0.102 0.008 <0.001***Premium increase NA indicator -0.093 0.069 0.176Attained age -0.001 0.001 0.140SexM 0.038 0.020 0.056.SexNUL -5.057 39.050 0.897Face amount 0.000 0.000 0.005**RiskClass – Preferred Nonsmoker 0.017 0.022 0.429RiskClass – Standard Nonsmoker 0.391 0.020 <0.001***RiskClass – StandardSmoker 0.274 0.034 0.000***RiskClass – Unknown 0.206 0.101 0.041*
Note: Model left incomplete for demonstration
Model validation – Age
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Model validation – Premium Increase
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Two-way lift chart
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Conclusion
• Predictive modeling can be a powerful tool for identifying key relationships in your data
• There are many different model types and approaches to choose from
• Predictive modeling is a convenient tool to modify existing techniques to reflect your own experience
• Always use a well-defined training and testing process
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Thank you
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AUGUST 28, 2019E
Al Klein - ModeratorValuation Actuaries Symposium – Session 76What can you learn from the data? What type of analytics should you use?
How to Use Predictive Modeling to Better Manage Your Life Insurance Inforce
What will you learn from this session?Case studies using different methodologies
BenMortality using logistic regressionLapse using Poisson regressionBrianMix of business using an algorithmic approachDetecting anomalies in the data using a non-traditional analytic approach
Themes to keep in mindWhat data issues are you interested in?What technique should you use to better understand this?Did you learn what you wanted from the data? If no:How can you manipulate the data to better understand it?Will another technique help more?Are there other considerations/reasons? If yes:Are you comfortable the results are valid and reasonable?What actions will you now take?
SOA 2016 Survey on Predictive Analytics.Other broad categories included Marketing and Underwriting
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INFORCE MANAGEMENT
PROGRAM IMPLEMENTED WORKING ON
NOT WORKING ON
BUT CONSIDERING
NOT WORKING ON AND NOT
CONSIDERINGTOTAL
Pre-lapse 7 6 6 9 29
PLT conservation mgmt. 2 7 8 11 28
Agent monitoring/mgmt. 2 6 11 7 26
Post-lapse 2 5 8 11 26
Targeted conversion 5 2 7 12 26
Other customer interaction 1 2 4 8 15
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Bio – Al Klein Principal and Consulting Actuary, Milliman, Buffalo Grove (Chicago), IL, since 2009
Responsible for industry experience studies at Milliman, mortality/longevity/life underwriting consulting, helping InsurTech companies enter the life insurance marketplace
Frequent national and international speaker on many topics
SOA activities: Chair of Underwriting Issues and Innovation Seminar planning committee, Chair of Accelerated Underwriting Practices and Mortality Improvement surveys, Chair of POG for Economic Costs of Opioid Epidemic paper, Member of Mortality and Longevity Steering Committee, Consistent Framework for Mortality Improvement Assumptions Team, Actuaries Longevity Illustrator Team, WILL (Workable Innovations for Living Longer) Contest Team, Mortality and Underwriting Survey Committee, 2015 Valuation Basic Table team
Other activities: Co-Vice Chair of the International Actuarial Association Mortality Working Group, Chair of MWG Research Projects Team, Drivers of Future Mortality and Underwriting Around the World research projects, Member of Longer Life Foundation Advisory Board
Awards: One of 2017 SOA Volunteers of the Year, Best paper for 2018 SOA Product Development Section contest on creative presentation of future technologies, SOA Outstanding Presentation awards in 2016 and 2018
Bachelor of Science degree in Actuarial Science and Finance, University of Illinois, Champaign/Urbana
Contact information: [email protected], 312-499-5731