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

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Session 62 TS, Predictive Modeling for Actuaries: Predictive Modeling

Techniques in Insurance


Yonasan Schwartz, FSA, MAAA


Jean-Frederic Breton


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




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



• Intro

• Predictive modeling background

• Case studies


What is predictive modeling?

Use of mathematical language to make

predictions about the future

Predictive model Input/ Predictors Output/ Response ,...) , , (T t DP f EL  



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


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)


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


• Greater availability of data and computing power than ever before

• Companies are investing in technology such as data warehouses and new admin systems


2013 Insurance predictive modeling survey


• Predictive models now widely used

• Pricing and underwriting are main applications

• Benefits seen on profitability, risk reduction and operational



• 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


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

Predictive analytics across the insurance lifecycle

In-force Policy Management

• Customer retention / lifetime value models

• Reserving

Claims Management

• Improve fraud detection • Improve exposure analysis


Some examples

Predicting S&P 500


• Multiple linear regression

• Feature selection and scenario analysis

Predicting S&P 500

(time series)

• ARIMA modeling • GARCH modeling

Predicting Customer Response


• 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

May-01 Feb-04 Nov-06 Aug-09 May-12 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 S&P 5 0 0

Realized vs Median Forecasted Path Original Data Simulated Data 0 10 20 30 40 50 60 70 80 90 100 P erc ent age

Bank Marketing Campaign Misclassification Rate Ne ural N et Logi stic Regress ion Discrim ina nt Analy sis k-nea rest N eig hbors N aive Bay es Suppo rt VM D ecisi on Trees T reeB agger Reduce d T B No Misclassified Yes Misclassified


Predictive modeling workflow

Known data

Known responses


Train the Model


New Data

Predicted Responses

Use for Prediction

Measure Accuracy

Select Model &


Import Data Explore Data


Prepare Data

Speed up Computations


Best practices and measures of quality


• 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


• R^2

• Standard deviation / variance • Mean Absolute Percentage Error • Classification

• Area under the Receiver Operating Characteristic (ROC) curve

• Cross-entropy • Confusion matrix


Short Example #1 – Predicting S&P 500

responses to economic data


• Predict changes to subaccount value as responses to changes in economic data


• 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 2001 2007 2013 600 800 1000 1200 1400 1600 1800 2000

S&P 500 Stock Price Index (Index, Daily) Response 20010 2007 2013 1000 2000 -5 0

5 Equity Market-related Economic Uncertainty Index (Index, Daily )

Leading Index f or the United States (Percent, Monthly ) 20010 2007 2013 2 4 6 8 10 0 2 4 6 8

10 10-Y ear Treasury Constant Maturity Rate (Percent, Daily )

3-Month Treasury Bill: Secondary Market Rate (Percent, Monthly ) 20010 2007 2013 2 4 6 8 10 0 2 4 6 8

10 3-Month Eurodollar Deposit Rate (London) (Percent, Daily )

3-Month London Interbank Of f ered Rate (LIBOR), based on U.S. Dollar (Percent, Daily ) 20010 2007 2013 1 2 50 100

150 U.S. / Euro Foreign Exchange Rate (U.S. Dollars to One Euro, Daily ) Japan / U.S. Foreign Exchange Rate (Japanese Y en to One U.S. Dollar, Daily )

20010 2007 2013 2 4 6 8 10 0 2 4 6 8 10 x 105

Civ ilian Unemploy ment Rate (Percent, Monthly ) Initial Claims (Number, Weekly , Ending Saturday )


Regression Modeling Techniques


Non-linear Reg. (GLM, Logistic) Linear Regression

Decision Trees Ensemble

Methods Neural


Short Example #2 – Time series modeling and

forecasting for the S&P 500 index


• Model S&P 500 time series as a

combined ARIMA/GARCH

process and forecast on test data


• Fit ARIMA model with S&P 500

returns and estimate parameters

• Fit GARCH model for S&P 500


• Perform statistical tests for time

series attributes e.g. stationarity

May-01 Feb-04 Nov-06 Aug-09 May-12

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 S& P 5 0 0

Realized vs All Forecasted Paths Original Data

Simulated Data

May-01 Feb-04 Nov-06 Aug-09 May-12

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 S& P 5 0 0

Realized vs Median Forecasted Path Original Data


Conditional Mean Models Conditional Variance Models AR- Autoregressive MA - Moving Average ARIMA – Integrated ARIMAX - eXogenous inputs ARCH GARCH EGARCH GJR Non-Linear Models

NAR Network


Short Example #3 – Marketing campaign


• Predict if customer would subscribe to

given product based on different



• Train a classifier using different models

• Measure accuracy and compare models

• Reduce model complexity

• Use classifier for prediction

0 10 20 30 40 50 60 70 80 90 100 P e rc en tage

Bank Marketing Campaign Misclassification Rate Ne ural N et Lo gist ic R egre ssi on Dis crim ina nt A naly sis k-n ea rest Ne igh bors Na ive Ba yes Sup po rt V M De cis ion Tree s Tre eB ag ger Re duc ed TB No Misclassified Yes Misclassified


Classification techniques



Non-linear Reg. (GLM, Logistic) Linear Regression

Decision Trees Ensemble

Methods Neural Networks Nearest Neighbor Discriminant

Analysis Naive Bayes

Support Vector Machines


Short Example #4 – Predict value of variable

annuity product


• Prototype such contract and

analyze its risks versus

return profile based on

Monte Carlo projections


• Fit a Geometric Brownian

Motion Stochastic

Differential Equation model

for the Equity indices in the



Conditional Mean Models Conditional Variance Models AR- Autoregressive MA - Moving Average ARIMA – Integrated ARIMAX - eXogenous inputs ARCH GARCH EGARCH GJR Non-Linear Models

NAR Network

Examples of models for time series data

Stochastic Differential Equation models


Predictive modeling techniques used in insurance

Supervised Learning (The target is known)

Unsupervised Learning (The target is unknown) Parametric


• Linear Regression • Time Series

• Generalized Linear Models

• Hazard Models

• Mixed Effect Models

• Cluster Analysis (i.e. K-means)

• Principal Components Analysis

Non-parametric • Neural Networks

• CART (Classification and Regression Trees)

• Random Forests

• MARS (Multivariate Adaptive Regression Splines)


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  (Ordinary Least Squares)

Identity:  g(µ)=µ Normal General Scoring Models

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)=(‐



Predictive analytics software

• Many packages for different

aplications, platform and modeling skills

Some packages used in insurance:

• Angoss KnowledgeStudio • Excel

• IBM SPSS Modeler • Mathematica


• Oracle Data Mining • R




Time (loss of productivity) Rapid analysis and application development

High productivity from data preparation, interactive  exploration, visualizations.

Extract value from data Machine learning, Financial

Depth and breadth of algorithms in classification,  clustering, and regression

Computation speed Fast training and computation

Parallel computation, Optimized libraries Time to deploy & integrate Ease of deployment and leveraging enterprise For eg, push‐button deployment into production Technology risk High‐quality libraries and support Industry‐standard algorithms in use in production Access to support, training and advisory services when  needed



• Intro

• Predictive modeling background

• Case studies


Predictive modeling workflow

Known data

Known responses


Train the Model


New Data

Predicted Responses

Use for Prediction

Select Model &


Import Data Explore Data


Prepare Data

Speed up Computations


Predictive modeling techniques used in insurance

Supervised Learning

(The target is known)

Unsupervised Learning

(The target is 




Linear Regression

Time Series

Generalized Linear Models

Hazard Models

Mixed Effect Models

Cluster Analysis 

(i.e. K‐means)

Principal Components 



Neural Networks

CART (Classification and 

Regression Trees)

Random Forests

MARS (Multivariate Adaptive 

Regression Splines)

Neural Networks


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


Case study 1 – Target marketing


• 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.


Propensity to Buy Model Health Risk Model Avoid marketing to those who  are likely to have a claim Avoid spending marketing time  and money on those who are  more likely to be not interested 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.

Target marketing

Building separate models that predict specific target variables can then be combined to achieve the desired business result

Low Score = Likely to be in  good health High Score = Likely to  have/develop health issues Low Score = Less likely to  need/buy insurance products High Score = more likely to  need/buy insurance products

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


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


Predictive  Model Data from Insurance  Applicant : • Part 1 & 2 Application • Telephone interview Underwriting  Rules • Obtain and analyze medical test results • Policy issued or denied • Processing time  ‐ several  weeks • Medical tests not required • Policy issued • Processing time  ‐ several days Low Risk – Expedited Issue Medium Risk – Traditional Underwriting

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

• 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 High Risk – Address Issues Date from Alternate  Sources: • MIB • MVR • Rx • Internal customer data • 3rd party marketing  data


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.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1 2 3 4 5 6 7 8 9 10 Decline Model Preferred Model Sample Lift Curves Decile Decile %  of  Populatio n 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1 2 3 4 5 6 7 8 9 10 Random Choice Model Results


0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10

Preferred Underwriting Model

Visualizing and interpreting results

• Advanced visualization can highlight strengths and weaknesses of the model

and identify areas for further investigation

55% (% of best  class in  general  population) Percent  of  Population Outliers Outliers Strong Lift


Predictive modeling development and validation

Train 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

Test Data • This dataset is an unbiased sample to help select the best predictive model

Validation Data • 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

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. Train 30% Test 30% Validation 40%

Modeling Data Iterative model building

Model  Implementation Model  Validation Ongoing  Performance Monitoring


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:


• 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


Case study 3 – Analyzing policyholder behavior for


• 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


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 Under Utilization • Continued under  utilization of the  withdrawal benefit will  leave money “on the table” • Allow further analysis of  reasons for under  utilization

Analyzing policyholder behavior for GMWBs

• 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?


• Refine valuation assumptions • Understand drivers of policyholder

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.

CART Marketing Product  Development GLM Underwriting Neural  Networks Retention Clustering Random  Forests Time Series/ Survival  Models Inforce  Management

• Develop product assumptions based on prior products

• Targeted marketing campaigns • Customer segmentation


• Enhance claims forecasting • Fraud detection

• Align customer retention with customer value • Streamline/reduce UW requirements


Considerations for developing an analytics



• Does your organization have the tools in place to capture data and develop


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”?


• Developing predictive analytics and modeling capabilities within an


Case study 4: The future?

Life Insurance  Policy Issued Health /Lifestyle feedback  Provided to p/h Predictive Model run annually on  all policies Policyholder  Chooses to  incorporate  feedback Premium Adjusted  / Lapse Decision Policyholder  incentive to  reduce risk Reduce tail risk with  Identify lifestyle  based risks after  policy underwritten  and issued Predictive  Model  Determines  UW class Application  completed

Future applications may not be bound by the traditional limits of life insurance and annuity products, and disruptions may occur from outside the industry.

Integrate  with Health/LTC  coverage Input to  Pricing other Lines  of Business Social Media Data Geospatial Data Positive  feedback/coaching  included in contract Disruption From  Non‐Traditional  Insurance Providers



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



• Intro

• Predictive modeling background

• Case studies