Session 62 TS, Predictive Modeling for Actuaries: Predictive Modeling Techniques in Insurance Moderator: Yonasan Schwartz, FSA, MAAA

Session 62 TS, Predictive Modeling for Actuaries: Predictive Modeling Techniques in Insurance Moderator: Yonasan Schwartz, FSA, MAAA Presenters: Jean-Frederic Breton David A. Moore, FSA, MAAA

Session 62: Predictive Modeling Techniques in Insurance Jean-Frederic Breton, Senior Financial Engineer, MathWorks David Moore, FSA, MAAA, Senior Technical Director, Nationwide

All models are wrong, but some are useful. George E. P. Box 1

Introductions Who we are: David Moore: FSA, MAAA, Senior Technical Director, Nationwide. Actuary with 15 years experience in life insurance, including 5 years in design and development of life insurance predictive analytics JF. Breton: BSc.Maths, MBA, Senior Financial Engineer now at MathWorks in NYC. 13 years of experience in finance in North America / Europe in Insurance and Banking with predictive modeling and risk management In this session: We will cover different best-practice predictive modeling techniques from a practical point of view (no theory today) Show how these can answer practical business questions such as what clientele should be targeted for a given product how much should be charged for a given contract feature how to optimize business processes such as underwriting triage At the conclusion of the session you will be able to: Understand how predictive models can help them answer a variety of business questions Describe common predictive modeling techniques in insurance Explain how these can be applied 2

Agenda Intro Predictive modeling background Case studies Q&A 3

What is predictive modeling? Use of mathematical language to make predictions about the future Examples Input/ Predictors Predictive model Output/ Response EL f ( T, t, DP,...) Trading strategies Electricity Demand 4

Why develop predictive models? Forecast rates/prices/returns Price complex contracts and guarantees Analyze impact of predictors (sensitivity analysis / stress testing) Gain economic/market insight And many more reasons 5

Relevant macro trends Available technology and large amount of data Increased need for customized products/services Pressure on top line of income statement (ref: 2013 SOA Annual Conference Session 180: Looking Toward the Future) 6

Historical perspective: predictive modeling in Property & Casualty vs. Life & Annuity P&C industry has matured much faster Life & Annuity Credit scores have been used to predict future P&C claims for over 20 years Short duration P&C products have limited tail risk compared to most life contracts Mortality studies can require several years of data to analyze Life and Annuity companies are now looking to analytics for strategic advantages Greater availability of data and computing power than ever before Companies are investing in technology such as data warehouses and new admin systems 7

2013 Insurance predictive modeling survey Impacts Predictive models now widely used Pricing and underwriting are main applications Benefits seen on profitability, risk reduction and operational efficiency Challenges Lack of sufficient data and skilled modelers Getting more data attributes Data prep and model deployment can often take 3 months Big Data is currently mainly leveraged by large insurers (Source: Earnix) 8

Predictive analytics across the insurance lifecycle Sales and Marketing Customer response modeling propensity to buy or renew Agent recruiting Pricing / Product Development Price optimization Risk Selection / Scoring Predictive underwriting UW triage Risk segmentation Experience Analysis True multivariate approach Efficient use of data In-force Policy Management Customer retention / lifetime value models Reserving Claims Management Improve fraud detection Improve exposure analysis Financial Forecasting 9

100 90 80 70 60 50 40 30 20 10 0 Bank Marketing Campaign Misclassification Rate No Misclassified Yes Misclassified Some examples Predicting S&P 500 (parametric) Multiple linear regression Feature selection and scenario analysis Predicting S&P 500 (time series) ARIMA modeling GARCH modeling Predicting Customer Response (non-parametric) Classification techniques Measure accuracy and compare models Predicting price and risk of VA contract (time series) Fit and simulate from a GBM model for the subaccount S&P 500 Realized vs Median Forecasted Path 1800 Original Data 1700 Simulated Data 1600 1500 1400 1300 1200 1100 1000 900 800 May-01 Feb-04 Nov-06 Aug-09 May-12 Percentage Neural Net Logistic Regression Discriminant Analysis k-nearest Neighbors Naive Bayes Support VM Decision Trees TreeBagger Reduced TB 10

Predictive modeling workflow Speed up Computations Select Model & Predictors Data Train the Model Use for Prediction Import Data Explore Data Prepare Data Known data Known responses Model Model New Data Predicted Responses 11 Measure Accuracy

Best practices and measures of quality Best-practices Split the available data between a training set and a testing set Try out and compare different models Measure the accuracy of the models Simplify your model when possible Some measures of accuracy Regression R^2 Standard deviation / variance Mean Absolute Percentage Error Classification Area under the Receiver Operating Characteristic (ROC) curve Cross-entropy Confusion matrix 12

Short Example #1 Predicting S&P 500 responses to economic data Goal Predict changes to subaccount value as responses to changes in economic data Approach Collect and clean up economic and financial market data Model S&P 500 index returns using multiple linear regression, predictor selection and model diagnostic techniques 2000 1800 1600 1400 1200 1000 800 Response S&P 500 Stock Price Index (Index, Daily) 2000 5 600 1000 0 2001 2007 2013 0-5 2001 2007 2013 10 10 8 8 6 6 4 4 2 2 0 0 2001 2007 2013 10 10 8 6 Predictors 4 4 2 2 0 0 2001 2007 2013 2 150 1 100 0 50 2001 2007 2013 x 10 5 10 10 8 8 6 6 4 4 2 2 0 0 2001 2007 2013 8 6 Equity Market-related Economic Uncertainty Index (Index, Daily ) Leading Index f or the United States (Percent, Monthly ) 10-Year Treasury Constant Maturity Rate (Percent, Daily ) 3-Month Treasury Bill: Secondary Market Rate (Percent, Monthly ) 3-Month Eurodollar Deposit Rate (London) (Percent, Daily ) 3-Month London Interbank Of f ered Rate (LIBOR), based on U.S. Dollar (Percent, Daily ) U.S. / Euro Foreign Exchange Rate (U.S. Dollars to One Euro, Daily) Japan / U.S. Foreign Exchange Rate (Japanese Yen to One U.S. Dollar, Daily ) Civ ilian Unemploy ment Rate (Percent, Monthly ) Initial Claims (Number, Weekly, Ending Saturday ) 13

Regression Modeling Techniques Regression Neural Networks Decision Trees Ensemble Methods Non-linear Reg. (GLM, Logistic) Linear Regression 14

Short Example #2 Time series modeling and forecasting for the S&P 500 index Goal Model S&P 500 time series as a combined ARIMA/GARCH process and forecast on test data S&P 500 11000 10000 9000 8000 7000 6000 5000 4000 3000 Original Data Simulated Data Realized vs All Forecasted Paths Approach Fit ARIMA model with S&P 500 returns and estimate parameters Fit GARCH model for S&P 500 volatility Perform statistical tests for time series attributes e.g. stationarity S&P 500 2000 1000 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 May-01 Feb-04 Nov-06 Aug-09 May-12 Original Data Simulated Data Realized vs Median Forecasted Path 800 May-01 Feb-04 Nov-06 Aug-09 May-12 15

Examples of models for time series data Conditional Mean Models AR- Autoregressive MA - Moving Average ARIMA Integrated ARIMAX - exogenous inputs Conditional Variance Models ARCH GARCH EGARCH GJR Non-Linear Models NAR Network NARX Network 16

Short Example #3 Marketing campaign Goal Predict if customer would subscribe to given product based on different attributes 100 90 Bank Marketing Campaign Misclassification Rate 80 70 Approach Train a classifier using different models Percentage 60 50 40 30 20 No Misclassified Yes Misclassified Measure accuracy and compare models Reduce model complexity 10 0 Neural Net Logistic Regression Discriminant Analysis k-nearest Neighbors Naive Bayes Support VM Decision Trees TreeBagger Reduced TB Use classifier for prediction 17

Classification techniques Regression Neural Networks Decision Trees Ensemble Methods Non-linear Reg. (GLM, Logistic) Linear Regression Classification Support Vector Machines Discriminant Analysis Naive Bayes Nearest Neighbor 18

Short Example #4 Predict value of variable annuity product Goals Prototype such contract and analyze its risks versus return profile based on Monte Carlo projections Approach Fit a Geometric Brownian Motion Stochastic Differential Equation model for the Equity indices in the subaccount 19

Examples of models for time series data Conditional Mean Models AR- Autoregressive MA - Moving Average ARIMA Integrated ARIMAX - exogenous inputs Conditional Variance Models ARCH GARCH EGARCH GJR Non-Linear Models NAR Network NARX Network Stochastic Differential Equation models Geometric Brownian Motion HWV, CIR, Heston, etc 20

Predictive modeling techniques used in insurance Parametric (Statistical) Non-parametric Supervised Learning (The target is known) Linear Regression Time Series Generalized Linear Models Hazard Models Mixed Effect Models Neural Networks CART (Classification and Regression Trees) Random Forests MARS (Multivariate Adaptive Regression Splines) Unsupervised Learning (The target is unknown) Cluster Analysis (i.e. K-means) Principal Components Analysis Neural Networks 21

Generalized linear models GLMs have become the most common tool for model development in life insurance as a result of their ability to accommodate forms other than normal, and for being relatively easy to explain Common GLM Applications Technique Link Function Distribution Application Classical Regression Identity: g(µ)=µ Normal General Scoring Models (Ordinary Least Squares) Logistical Regression Logit: g(µ)= log[µ/(1 µ)] Binomial Binary Target Applications (i.e. Retention) Frequency Modeling Log: g(µ)=log(µ) Poisson Negative Binomial Count Target Variable Frequency Modelnig Severity Modeling Inverse: g(µ)=( 1/µ) Gamma Size of claim modeling Severity Modeling Inverse Squared: g(µ)=( 1/µ^2)) Inverse Gaussian Size of claim modeling 22

Predictive analytics software Many packages for different aplications, platform and modeling skills Some packages used in insurance: Angoss KnowledgeStudio Excel IBM SPSS Modeler Mathematica MATLAB Oracle Data Mining R SAS Predictive Analytics 23

Challenges and what to look for in a solution Challenges Time (loss of productivity) Extract value from data Computation speed Time to deploy & integrate Technology risk Solution Rapid analysis and application development High productivity from data preparation, interactive exploration, visualizations. Machine learning, Financial Depth and breadth of algorithms in classification, clustering, and regression Fast training and computation Parallel computation, Optimized libraries Ease of deployment and leveraging enterprise For eg, push button deployment into production High quality libraries and support Industry standard algorithms in use in production Access to support, training and advisory services when needed 24

Agenda Intro Predictive modeling background Case studies Q&A 25

Predictive modeling workflow Speed up Computations Select Model & Predictors Data Train the Model Use for Prediction Import Data Explore Data Prepare Data Known data Known responses Model Model New Data Predicted Responses 26 Measure Accuracy

Predictive modeling techniques used in insurance Parametric (Statistical) Non parametric Supervised Learning (The target is known) Linear Regression Time Series Generalized Linear Models Hazard Models Mixed Effect Models Neural Networks CART (Classification and Regression Trees) Random Forests MARS (Multivariate Adaptive Regression Splines) Unsupervised Learning (The target is unknown) Cluster Analysis (i.e. K means) Principal Components Analysis Neural Networks 27

Case study 1 Target marketing Business Problem How do I know who to target to buy a new product? Business Case for Building a Predictive Model Many companies already use analytics in their marketing areas to identify those with a higher propensity to buy insurance products Identifying those customers who are also more likely to be profitable can lead to more effecting marketing spend Preferred Model GLM with Logistical Regression The target outcome is binary, either you want to market to a person or you don t 28

Case study 1 Target marketing Data: Historical product information to identify the profile of historically profitable customers Marketing data to identify those with a need for insurance product and/or those with the means to pay for it Underwriting data (MIB, MVR, & Prescription Drug database) identify if they are likely to pass the underwriting requirements for a product Additional Considerations Building multiple models is often necessary to predict multiple factors needed to determine the value of a customer. i.e. propensity to buy, propensity to lapse, need for insurance, health status, etc. 29

Target marketing Building separate models that predict specific target variables can then be combined to achieve the desired business result Low Score = Less likely to need/buy insurance products Propensity to Buy Model High Score = more likely to need/buy insurance products High Score = Likely to have/develop health issues Health Risk Model Low Score = Likely to be in good health Avoid spending marketing time and money on those who are more likely to be not interested Avoid marketing to those who are likely to have a claim Focus Marketing efforts on the population who are more likely to be buy a policy, and who present less mortality/morbidity risk to the insurer. The decision on where to draw the line for which model scores lead to which marketing actions is not arbitrary, it should be optimized based on the cost of marketing and the potential returns from the business issued based on the model Discussion Question what if you have no historical data to base your model on? 30

Case study 2 - Predicting life insurance underwriting decisions Life Insurance products protect against mortality, however the mortality experience of a block of data can take years to be credible As an alternative, insurers have used underwriting class as a proxy for the true mortality, as it represents the expected mortality at the time of issue Base model is a GLM with underwriting class as the target variable As preserving mortality is key, additional work if often needed on groups of outliers This can include: Use of multiple GLMs CART analysis Clustering 31

Sample underwriting triage process Low Risk Expedited Issue Data from Insurance Applicant : Part 1 & 2 Application Medical tests not required Policy issued Processing time several days Telephone interview Medium Risk Traditional Underwriting Date from Alternate Sources: MIB MVR Rx Internal customer data 3rd party marketing data Predictive Model Underwriting Rules Obtain and analyze medical test results Policy issued or denied Processing time several weeks High Risk Address Issues If data or the model indicates the case should be declined, obtain confirmation (i.e. test results) to decline the application Route to more experienced UW ers to handle Potential Benefits of Underwriting Triage Eliminate time-consuming, expensive and physically invasive tests for certain applicants Improved underwriting operational efficiency assign complex cases to best underwriters Streamline application review process 32 Improve ease of doing business for agents and applicants

Visualizing and interpreting results Lift is a measure of the performance of a model at predicting or classifying cases as having an enhanced response (with respect to the population as a whole), measured against a random choice targeting model. Decline Model Sample Lift Curves Preferred Model % of Population 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1 2 3 4 5 6 7 8 9 10 Decile 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1 2 3 4 5 6 7 8 9 10 Decile Random Choice Model Results 33

Visualizing and interpreting results Advanced visualization can highlight strengths and weaknesses of the model and identify areas for further investigation Preferred Underwriting Model 100% Outliers 90% 80% Percent of Population 70% 60% 50% 40% Strong Lift 55% (% of best class in general population) 30% 20% 10% Outliers 0% Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10 Worst Scores Model Score Best Scores Best Underwriting Class 34

Predictive modeling development and validation When developing a model, it is important to use an accepted validation methodology to evaluate the model. This improves the likelihood the model will produce accurate feedback going forward. Modeling Data Iterative model building Train 30% Test 30% Model Validation Model Implementation Ongoing Performance Monitoring Validation 40% 35 Train Data Test Data Validation Data Algorithm development is an iterative process train data is run through numerous modeling techniques and potentially hundreds of algorithms to determine the optimal model This dataset is an unbiased sample to help select the best predictive model This represents a hold out sample which is not used to either develop or test the model. Once the final model is selected, this data is used to validate the results on a blind sample and to confirm that there is no over fitting

Refining the model Adding synthetic variables The relationship between existing variables can provide valuable insight to the model that is not present when using these variables in isolation Examples: BMI Is the contract owner the annuitant/insured? Refining the results with additional models or rules Underwriting rules Principle Components Analysis Sum of GLM models CART analysis Clustering In the underwriting triage example, refinements can purify the cohort that is recommended for expedited underwriting, and reduces the risk of outliers 36

Case study 3 Analyzing policyholder behavior for GMWBs Business Problem Can I predict future cash flows on a variable annuity by identifying which policyholders are more likely to maximize the value of the GMWB (Guaranteed Minimum Withdrawal Benefit) rider they have purchased? Business Case for Building a Predictive Model Segmenting a population based on policyholder behavior can enable you to set dynamic assumptions to more accurately predict future cash flows. Potential benefits may include improved product pricing, lowering reserves, and reduced hedge breakage Background on product A GMWB rider offers the buyer lifetime income protection by guaranteeing the withdrawals they can take out of their VA account. Typically there is a maximum annual withdrawal (5-7% of base value at the start of withdrawals). Taking out too much money weakens the guarantee or erodes your base account value, while not taking out enough money means you are not taking advantage of the full guarantee. If the contract holder is not maximizing the value of their rider, there is likely a reason (i.e. large immediate financial need) that we can use analytics to gain more insight in to. Models to develop 1) Time to first withdrawal model using a survival model 2) Efficient use of rider model using GLM and binomial link function 37

Analyzing policyholder behavior for GMWBs Under Utilization Continued under utilization of the withdrawal benefit will leave money on the table Allow further analysis of reasons for under utilization GMWB User Segments Optimal User Contract owner desires to maximizes the value of their rider guarantee Default assumption when developing products Over Utilization Large withdrawals show the immediate need for money, and perhaps limited savings elsewhere Need to identify if large withdrawals are due to a onetime or ongoing need Target Variables Modeling when withdrawals begin can be done with a hazard or survival model Modeling optimal behavior requires us to define what is optimal; we can identify segments of the population that exhibit different withdrawal patterns Predictive Model A logistic regression can be used to identify the segment each individual is most likely a member of Next Steps Align assumptions with policyholder segmentation Understand transitions between states, are some groups static while others vary their WD patterns? Investigate additional hypothesis, i.e. does one large withdrawal make you more likely to do it again in the future? 38

Other modeling techniques for insurance Many different modeling techniques can be applied across the insurance lifecycle to solve different business problems; GLMs remain the most popular and flexible of the options available to us. GLM Product Development Develop product assumptions based on prior products CART Marketing Targeted marketing campaigns Customer segmentation Neural Networks Underwriting Streamline/reduce UW requirements Audit UW process Clustering Retention Align customer retention with customer value Random Forests Claims Enhance claims forecasting Fraud detection 39 Time Series/ Survival Models Inforce Management Refine valuation assumptions Understand drivers of policyholder behavior

Considerations for developing an analytics program Tools Does your organization have the tools in place to capture data and develop analytics? Human Resources Do you have people with appropriate business and technical skills to design, build, and implement advanced analytical solutions? Big Data Do you have a plan in place to deal with Big Data? Patience Developing predictive analytics and modeling capabilities within an organization can take time and requires a long term vision and plan 40

Case study 4: The future? Future applications may not be bound by the traditional limits of life insurance and annuity products, and disruptions may occur from outside the industry. Application completed Input to Pricing other Lines of Business Integrate with Health/LTC coverage Disruption From Non Traditional Insurance Providers Predictive Model Determines UW class Life Insurance Policy Issued Identify lifestyle based risks after policy underwritten and issued Predictive Model run annually on all policies Health /Lifestyle feedback Provided to p/h Policyholder Chooses to incorporate feedback Positive feedback/coaching included in contract Policyholder incentive to reduce risk 41 Social Media Data Geospatial Data Premium Adjusted / Lapse Decision Reduce tail risk with adjustable premium

Takeaways Predictive Modeling is still in the early stages of maturity in the Life and Annuity space, although the level of interest in developing and using predictive modeling continues to grow rapidly Big Data and computing power alone are not enough, developing functional models is an iterative process that requires knowledge of your business and of statistical modeling techniques, and an understanding of how insights from the data can be applied to insurance in order to grow the business and/or manage risk 42

Agenda Intro Predictive modeling background Case studies Q&A 43

Q&A Questions? 44