Combining Linear and Non-Linear Modeling Techniques: EMB America. Getting the Best of Two Worlds

EMB

America

Getting the Best of Two Worlds

Combining Linear and Non-Linear

Modeling Techniques:

Outline

Who is EMB?

Insurance industry predictive modeling applications

EMBLEM – our GLM tool

How we have used CART with EMBLEM

Case studies

EMB Worldwide

Global network of p&c insurance consultants servicing

clients throughout the world

Consulting Services Offered

Business Planning Regulatory Support

& Law Analysis

Reserve Analysis & Opinion Letters Reinsurance Program Analysis Expert Witness Testimony Software Development & Software Support

EMB

State-of-the-Art Software

EMB’s suite of software products cover all aspects of

personal and commercial lines of insurance

Igloo Professional

Financial simulation engine for risk modeling ExtrEMB Dynamic parameterization for risk modeling EMBLEM

GLM software for risk, marketing, and claims analysis Rate Assessor Pricing implementation software Classifier Categorization software for high-dimension variables (e.g., territory)

ResQ Professional

Complete loss reserving tool

PrisEMB

Reinsurance and large account pricing

RePro

Management information analysis software for excess of loss insurance

We use EMBLEM, a GLM tool, for our predictive modeling

needs

Why?

Predictive Modeling in the Insurance Industry

Primary application:

- Estimating the cost of the product they sell (insurance)

Two steps:

1. Reserving = estimating the cost of outstanding insurance claims

2. Pricing = estimating the cost of future insurance coverage

Secondary applications:

- Retention Modeling = probability that a policyholder will renew

- Conversion Modeling = probability that a prospective policyholder will purchase a policy

- Price Optimization

- Claim fraud detection

Estimating the Cost of Insurance

Goal is to develop a unique rate for every risk

- Don’t think in terms of good/bad risks

- State Farm/Allstate vs GEICO/Progressive

- Quickly exhausts the data

• credibility / variability / stability

Risks are described by the predictor variables, not the target

- Need to have a mapping of the predictor variable levels to a target value – not the other way around

• Other way around makes it difficult to derive impact of individual

predictor variables

• Important because actual data often does not describe all

Estimating the Cost of Insurance

Highly regulated marketplace

- Restrictions

• Predictors can and cannot use

Ü Credit score

• Rules on values for the predictors

Ü Ages 65+ relativities cannot be >110% of ages 40-60

Ü Maximum rate change between adjacent territories

• Rules on predictor order and magnitude of importance

Ü CA Sequential Analysis (driving record > annual mileage >

years held license)

- Regulatory Approval

• Rates need to be supported

Estimating the Cost of Insurance

Response variable is continuous/discrete function

No single trial/outcome

- Trial is measured in terms of time

- Actual policy length varies tremendously because of changes

• marital status • new car • moved Density: Severity 0 200 400 600 800 1,000 1,200 1,400 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 Range De n s it y Severity Frequency: Frequency 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000 0 1 2 3 4 Range Fr e qu e n c y Frequency

- Gamma consistent with severity modeling, or even Inverse Gaussian

- Poisson consistent with frequency modeling

Solution?

In 1996, EMB designed EMBLEM to provide access to GLM for statisticians and non-statisticians pricing personal and commercial insurance

EMBLEM revolutionized the use of GLM’s, enabling analysis that was previously either impossible or too time-consuming to be worth attempting

EMBLEM is now used by over 100 insurance companies globally:

- 18 of the top 20 personal auto writers in the UK

- 50 companies in the US including 8 of the top 10 personal auto writers

Fastest GLM tool with the capability to model millions of observations in seconds with a host of diagnostic tools:

- Graphical, practical, statistical, automated.

- Stand-alone software package that can be integrated with a variety of

external software including SAS®_.

- Microsoft® _{Visual Basic}® _{for Applications provides ultimate flexibility.}

GLM characteristics work to our advantage

- Exponential family does an excellent job of describing the underlying components of insurance losses

- Output of the model is in the form of Beta parameters which can easily be converted to rate relativities

- EMBLEM is not automated

• User has complete control over the model structure

• Complete diagnostic tools to assist the modeler with decisions

Current Status in Insurance Marketplace

In terms of estimating the cost of insurance:

- UK has embraced predictive modeling

• Experienced with its techniques

• Knowledgeable with the factors that tend to be predictive

- US is learning about predictive modeling

• Saturation with big players in personal lines marketplace

Ü Companies not using predictive modeling techniques are

being adversely selected against

Ü Now expanding dimensionality of databases

• Still fairly new concept in commercial lines marketplace

Ü Big players are using techniques but historical rating

Current Status in Insurance Marketplace

Result?

- UK is expanding into secondary applications

• Retention modeling

• Conversion modeling

• Price optimization

• Claim fraud detection

- Because Predictive Modeling has been around for some time

in the UK, the datasets are getting larger in terms of the number of predictors to evaluate

- Experienced US companies are beginning to evaluate the

secondary applications

How does CART fit into this?

- As we transition into the secondary applications we move from modeling a continuous function to a binary function

• Tree-based techniques can add value to the analysis

Retention and Conversion modeling

- Accept/Reject target variable

- Desirable smooth surface

- Price optimization integrates these with premium models

Marketing and Fraud detection

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Using CART and EMBLEM

- Goal is to play off of the strengths of each tool

CART Strengths

- Automatic separation of relevant from irrelevant predictors

- Easily rank-orders variable importance

- Automatic interaction detection (requires additional work)

- Captures multiple structures within a dataset rather than a single dominant structure

- Can handle missing values and is impervious to outliers

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EMBLEM Strengths

- User has control over the model structure

- Ease of communication/conceptualization – effects of each explanatory variable is transparent

- Provides predicted response values for new data points

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CART

EMBLEM

Incorporating time/seasonality trend effects Implementation of results

Speakers Note

Both CART and EMBLEM are excellent tools both of which

produce consistent results in similar situations

- This is not an exercise of seeing which is better

The purpose of this discussion is to show how efficiencies

can be gained in the modeling process

- As datasets get larger in terms of the number of predictors time becomes a crucial element

Case Study #1 – US Dataset

Retention modeling assignment

- 97,227 observations

• each observation represents one trial/outcome

• split 50/50 between training/test datasets

- 11 predictors

Case Study #1

Modeling Process

- Started with Forward Entry Regression

• Automated process

• Used Chi-Squared statistic for testing significance

• Took about 30 minutes to run

- Significant factors (8) • Rating Area • Vehicle Category • Age • NCD • Driver Restriction • Vehicle Age

• Change Over Last Year’s Premium

Forward Entry Regression

Build a Model with no factors and add based on

prespecified criteria regarding improvement in model fit:

0.1% 18,594 12,371.45 Mean + Time 18 0.2% 18,595 12,370.30 Mean + MTA Indicator

17 . . 18,576 18,581 18,570 18,594 18,596 Degrees of Freedom 9,997.75 12,365.50 12,214.88 12,377.02 12,380.23 Deviance 0.0% Mean + Vehicle Age

4

47.1% Mean + Rating Area

3

0.0% Mean + Policyholder Age

2 20.1% Mean + Gender 1 Mean Variables Base

Chi Squared Compare to Base Model

Add the factor that performed the best on the Chi Square

test. (Policyholder Age)

Iterate process with the new base model until no further

factors indicated removal

Case Study #1

Compared results with CART/TreeNet

- Significant factors were essentially the same

- Model predictiveness was the same (ROC = 0.7)

Interactions

- no significant interactions were found by EMBLEM or CART

Test Dataset

Case Study #2 – UK Dataset

Retention modeling assignment

- 198,386 observations

• each observation represented one trial/outcome

• split 50/50 between training/test datasets

- 135 predictors

Case Study #2

Forward Entry Regression

- Found 57 predictors to be significant

- Took a weekend to run

Comparison to CART/TreeNet

- Found 24 significant predictors

- Top 15 based on variable importance were also found by

EMBLEM

- Correlations with the rest of the predictors

Through the modeling process we reduced the number of

predictors to 26

Case Study #2

Interactions

- We relied on indications from CART/TreeNet

- 6 interactions were identified and included in the model

EMBLEM Results

- Training ROC = .862

Other Expected Synergies

Variable importance

Segmentation

Segmentation

CART excels at identifying different segments in data CART may also help determine where to segment data

Segmentation is a useful alternative to fitting many interactions

Example: in a automobile insurance renewal problem, a CART analysis showed several occurrences of a split between those policyholders with just one years duration and those with a greater duration.

This suggests segmenting the data into two parts: Policies renewing with one year duration

Super-Profiling

After a GLM model is constructed use CART to model the

residuals to see if any pattern exists

- If a pattern is discovered, go back to the model structure and incorporate the findings