**Session 62 TS, Predictive Modeling for Actuaries: Predictive Modeling **

**Techniques in Insurance **

**Moderator: **

**Yonasan Schwartz, FSA, MAAA **

**Presenters: **

**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

### useful.”

### 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

### Agenda

• 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*

### Examples

### 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

advantages

• 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

### •

**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

• **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**

*(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

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

Model

### Train the Model

Model

New Data

Predicted Responses

### Use for Prediction

### Measure Accuracy

### Select Model &

### Predictors

Import Data Explore Data### Data

Prepare Data### Speed up Computations

### 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

### 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 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

**Regression**

**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

### •

**Goal**

### • Model S&P 500 time series as a

### combined ARIMA/GARCH

### process and forecast on test data

### •

**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

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

### •

**Goal**

### • Predict if customer would subscribe to

### given product based on different

### attributes

### •

**Approach**

### • 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

**Regression**

**Classification**

**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

### •

**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

**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

(Statistical)

• 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)=(‐

1/µ^2))

### 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

**Challenges**

**Solution**

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

### Agenda

• Intro

• Predictive modeling background

• Case studies

### Predictive modeling workflow

Known data

Known responses

Model

### Train the Model

Model

New Data

Predicted Responses

### Use for Prediction

### Select Model &

### Predictors

Import Data Explore Data### Data

Prepare Data### Speed up Computations

### Predictive modeling techniques used in insurance

### Supervised Learning

### (The target is known)

### Unsupervised Learning

### (The target is

### unknown)

### Parametric

### (Statistical)

### •

### 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)

### •

### 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

### •

### 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.

**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:

• 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

### 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

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

Claims

• Enhance claims forecasting • Fraud detection

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

### 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

### 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**

### 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

### Agenda

• Intro

• Predictive modeling background

• Case studies