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University of MinnesotaDecember 3rd, 2010

Nathan Hubbell, FCASJohn Renze, PhD, FCAS

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Agenda

• Travelers– Broad Overview– Analytics Career Opportunities

• Predictive Modeling– Generalized Linear Models (GLM’s)

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• Offers property and casualty solutions to individuals and companies of all sizes

• Second-largest commercial insurer in the U.S.

• Second-largest personal insurer through the independent agency channel

• No. 98 on the Fortune 500 list of largest U.S. companies

• Representatives in every U.S. state, Canada,Ireland and the United Kingdom

• A member of the Dow Jones Industrial Average – the only insurance company on the list

Revenue of $25 billion and total

assets of $110 billion in fiscal year 2009

About Us

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Travelers – 2007The company name changed to The Travelers Companies, Inc. and began trading on the New York Stock Exchange under the symbol TRV. The 137-year-old insurance icon, the red umbrella, was reinstated.

St. Paul Travelers – 2004The St. Paul and Travelers merged on April 1, 2004 formingThe St. Paul Travelers Companies, Inc.

Company HistoryTravelers – 1864J.G. Batterson and nine others formed Travelers Insurance Company for the purpose of insuring travelers against death or injury while journeying by railway or steamboat.

The Saint Paul – 1853Seeing the need for a local insurance company, Alexander Wilkin and 16fellow Saint Paul businessmen founded St. Paul Fire and Marine Insurance.

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Our Organization

• Business Insurance: Offers a broad array of property casualty, specialty insurance and related services to businesses of all sizes.

• Financial, Professional & International Insurance: Includes international products and surety, crime and financial liability products that use credit-based underwriting processes.

• Personal Insurance: Offers products including automobile, homeowners, renters and condominium policies to individual consumers.

• Claim: Includes 13,000 trained Claim professionals in four countries and all 50 states who respond to customers 24 hours a day, seven days a week, 365 days a year.

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What is insurance and what good does it serve?

Insurance restores individuals to the financial state they were in prior to a loss (e.g. car accident; tree fell on house)

For this benefit, customers pay a premium to the insurance companyIf a customer doesn’t have a loss, then their premiumA. Helps the insurance company cover the loss another customer did haveB. Keeps the insurance company functioning so it can continue providing this service

If the customer does have a loss, it’s the other insureds that are helping them!

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Analytics at Travelers – Who are we?

Across the four business units, we form a large (100+) and diverse community of Ph.D., Masters and Bachelors holders in the following disciplines:

mathematicsstatisticsphysicsactuarial sciencecomputer sciencebusiness

… and more!

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What makes Travelers special?

Teamwork isn’t a buzzword here – it’s real and we live it

• We share information & technology openly with each other• Learning something new can be as simple as asking a local expert; they

make the time, despite busy schedules• We each have a unique combination of strengths; we are valued for them

and our managers help us grow into the careers we desire

Analytics at Travelers – Who are we?

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Analytics at Travelers – What do we do?

We ask and answer questions requiring sophisticated analyses

• How much will it cost to insure a customer?• How expensive will this claim be?• How likely is it that this customer will purchase our product?• How many claims adjusters will we need in two years?• What new statistical methods will help move our business into the future?

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Why are these questions hard?

Example: How much it costs to insure an auto customer

It’s impossible to predict if someone is going toA. Get into an accidentB. The type of accident (telephone pole, another vehicle)C. How bad the accident will be

But if we have enough customers, we can start to group them… in group A) we expect 1 / 10 to get into an accident, costing on average $1000in group B) etc.

Analytics at Travelers – What do we do?

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Why it matters…

The more finely we group, the more accurate the price. In that case:

1. If our competitors charge more, the customer will choose us and we will grow profitably

2. If our competitors charge less, the customer will choose them and they’ll grow unprofitably

Either way, we win! The trick is finding the right groups, and getting the right price for them…

Analytics at Travelers – What do we do?

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Analytics at Travelers - Methodologies

To stay ahead of our competitors, we sift through the literature searching for the most applicable techniques. Some examples:

– GAMs– Elastic net & adaptive LASSO– MARS– Gradient boosted trees

We pick the methods that have real-world value to our business and give us the competitive edge

We do a significant amount of proprietary methodology development internally

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Analytics at Travelers - Technology

We have millions of customers. To support this volume of data and facilitate the use of the latest methodologies, we rely on cutting-edge technology

Teradata data warehouses – hundreds of TB at our fingertips!

Multi-processor linux servers for analytic software• SAS• R• Salford Systems• Custom software (C++, FORTRAN)• …and more!

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Analytics at Travelers – Why us?

We are at the cutting-edge

We grow our people; we give them the training and opportunities they need to move their careers ahead

We are a team – it’s our combined focus that makes Travelers the leader of the industry that we are today.

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Predictive Modeling

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• Using Generalized Linear Models (GLM’s) and other statistical methods to predict exposure to loss at detailed level.

– Recently, property-casualty insurance companies have embraced predictive modeling as a strategic tool for competing in the marketplace.

• Originally introduced as a method of increasing precision for personal auto insurance pricing• Extended to homeowners and commercial lines• Today, it is applied in areas such as marketing, underwriting, pricing, and claims management

Predictive Modeling

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How do you differentiate your rates?

Automobile– Age– Gender– Marital status– # vehicles– # drivers– Home policy– Driving record– Years Licensed– Limits– Prior Insurance– Student/Nonstudent– Location (Garage/driven)– Annual Mileage

Homeowners– Age of home– # occupants– Primary / Secondary– Prior claim experience– Construction– Protection– Roof Type– Location (CAT?)– Amount of Insurance– Auto Policy– Responsibility of owner

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How do you set the prices?

• Old Way:

– Group data by class class relativities– Sort data into age groups age relativities– Group data by territory territorial relativities– Rating factor = class x age x territory

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What is wrong with the old way?

ExampleSize of car Age

• A young driver of a small car would be charged • 4.237 x 3.325 = 14.088

• times what an old driver of a large car would be charged.

• Important point: Some of this effect is double-counted, as size of car is correlated with age.• (numbers are illustrative only)

Class Claim Count

Exposures (number of cars)

Frequency (probability of a claim)

Relativity

Large cars 15 400 0.038 1Medium cars

110 1700 0.065 1.725

Small cars 143 900 0.159 4.237

Class Claim Count

Exposures (number of cars)

Frequency (probability of a claim)

Relativity

Old 80 1800 0.044 1Young 188 1200 0.157 3.325

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Possible Solution: Multiple Linear Regression

• E[Y] = a0 + a1X1 + …+ anXn

• Two Key Assumptions:– Y is Normally distributed random variable.– Variance of Y is constant (homoscedastic).

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Problems With Regression – Part I

• Y is NOT normally distributed.

– Number of claims is discrete– Claim sizes are skewed to the right– Probability of an event is in [0,1]

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Problems With Regression – Part II

• Variance of Y is NOT constant.

– Varies by expected loss.• High frequency losses have less variance.• High severity losses have more variance.

– Varies by exposure.

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Problems With Regression – Part III

Nonlinear relationship between X’s and Y’s.Example: Age of driver

(numbers are illustrative only)

0

0.5

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1.5

2

2.5

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3.5

Driver Age

Lo

ss R

elat

ivit

y

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Generalized Linear Models (GLMs)

• E[Y] = g-1(a0 + a1X1 + …+ anXn)

• Fewer restrictions:– Non-linear relationships.

• g(x) = x Additive model• g(x) = exp(x) Multiplicative model• g(x) = 1 / (1+exp(x)) Logistic model

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Generalized Linear Models (GLMs)

• E[Y] = g-1(a0 + a1X1 + …+ anXn)

• Fewer restrictions:– Y can be from any exponential family of distributions.

• Poisson (number of claims)• Binomial (probability of renewing)• Gamma (loss severity)

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Generalized Linear Models (GLMs)

• E[Y] = g-1(a0 + a1X1 + …+ anXn)

• Fewer restrictions:– Variance depends on the expected mean.

• Normal: Variance is constant.• Poisson: Variance equals mean.• Gamma: Variance equals mean squared.

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Generalized Linear Models (GLMs)

• What’s the catch?

– No closed form solution.– Use maximum likelihood estimation.

• Iterative process.• Make a guess and linearize.• Solve the linear problem to find next guess.

– Increased computational complexity.

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Key Steps in Model Building – Part I• What are you modeling?

• How will you implement?

• Gather and clean internal data.

• Link other sources: internal and external.

• Create training and validation sets

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Key Steps in Model Building – Part II• Build Model on Training Set

• Univariate analysis – statistically test each predictor• Build multivariate models using significant predictors

• Select best multivariate predictive model

Keep most relevant predictors

Principle of parsimony – simplicity is good

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Key Steps in Model Building – Part III

• Measure predictive power on validation set

• Was training set over fit?

• Peer review

• Implement

• Post-implementation monitoring

• Adjust with new knowledge