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2. University of Minnesota December 3 rd, 2010 Nathan Hubbell, FCAS John Renze, PhD, FCAS

3. 3 Agenda Travelers –Broad Overview –Analytics Career Opportunities Predictive Modeling –Generalized Linear Models (GLM’s)

4. 4 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

5. 5 Travelers – 2007 The 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 – 2004 The St. Paul and Travelers merged on April 1, 2004 forming The St. Paul Travelers Companies, Inc. Company History Travelers – 1864 J.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 – 1853 Seeing the need for a local insurance company, Alexander Wilkin and 16 fellow Saint Paul businessmen founded St. Paul Fire and Marine Insurance.

6. 6 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.

7. 7 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 company If a customer doesn’t have a loss, then their premium A.Helps the insurance company cover the loss another customer did have B.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!

8. 8 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: mathematics statistics physics actuarial science computer science business … and more!

9. 9 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?

10. 10 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?

11. 11 Why are these questions hard? Example: How much it costs to insure an auto customer It’s impossible to predict if someone is going to A.Get into an accident B.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 $1000 in group B) etc. Analytics at Travelers – What do we do?

12. 12 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?

13. 13 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

14. 14 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!

15. 15 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.

16. 16 Predictive Modeling

17. 17 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

18. 18 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

19. 19 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

20. 20 What is wrong with the old way? Example Size 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)

21. 21 Possible Solution: Multiple Linear Regression E[Y] = a 0 + a 1 X 1 + …+ a n X n Two Key Assumptions: –Y is Normally distributed random variable. –Variance of Y is constant (homoscedastic).

22. 22 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]

23. 23 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.

24. 24 Problems With Regression – Part III Nonlinear relationship between X’s and Y’s. Example: Age of driver (numbers are illustrative only)

25. 25 Generalized Linear Models (GLMs) E[Y] = g -1 (a 0 + a 1 X 1 + …+ a n X n ) Fewer restrictions: –Non-linear relationships. g(x) = x  Additive model g(x) = exp(x)  Multiplicative model g(x) = 1 / (1+exp(x))  Logistic model

26. 26 Generalized Linear Models (GLMs) E[Y] = g -1 (a 0 + a 1 X 1 + …+ a n X n ) Fewer restrictions: –Y can be from any exponential family of distributions. Poisson (number of claims) Binomial (probability of renewing) Gamma (loss severity)

27. 27 Generalized Linear Models (GLMs) E[Y] = g -1 (a 0 + a 1 X 1 + …+ a n X n ) Fewer restrictions: –Variance depends on the expected mean. Normal: Variance is constant. Poisson: Variance equals mean. Gamma: Variance equals mean squared.

28. 28 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.

29. 29 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

30. 30 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

31. 31 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