Data Mining Applications in P&C Insurance

1. Data Mining Applications in P&C Insurance CASE Spring Meeting April 12, 2005 Lijia Guo, PhD, ASA, MAAA University of Central Florida

2. Agenda • Introductions to data mining modeling • Understanding the data mining process • Data mining (DM) techniques • Applications in P&C Insurance • Case Study Guo

3. Introduction – What is Data Mining? • Process of exploration and analysis of large quantities of data in order to discover meaningful patterns and rules. • Uses a variety of data analysis tools to discover relationships that may be used to make valid predictions. • It is not a magic wand: • Must know your business • Understand your data • Understand the analytical methods Guo

4. Introduction - DM Modeling • An information discovery process. • Knowing your goals • Understanding your data • Choosing the right methods • Understanding the limitations • Validation and testing • Make crucial business decisions Guo

5. Define the Goal Understand the Economics Identify Data Sources Prepare Data Transform Data Apply DM Models IMPLEMENT Validate DM Models Introduction – DM Process Guo

6. Introduction – DM Goals • Identifying responsive potential customers • Identifying existing customers that more likely to terminate • Identifying high risk purchaser • Identifying the factors that cause large claims • Identifying interactions among risk factors Guo

7. Introduction – DM Process Guo

8. DM Techniques • Decision Trees • Logistic regression • Neural Networks • Fuzzy Logics • Genetic Algorithms • Clustering • Associated discovery • Sequence Discovery • Bayesian analysis • Visualization Hybrid algorithms Guo

9. DM Techniques -- Decision Trees • What are decision trees • Classify observations based on the values of nominal, binary, or ordinal targets • Predict outcomes for interval targets • Predict the appropriate decision when you specify decision alternatives Guo

10. DM Techniques -- Decision Trees Example Guo

11. DM Techniques -- Decision Trees • Strengths and weaknesses • Insights into the decision-making process • Efficient and is thus suitable for large data sets • Relatively unstable • Difficult to detect linear or quadratic relationships Guo

12. DM Techniques -- Logistic regression • What is Logistic regression • How Logistic regression works • Odds ratios • Each dependent variable affects logit linearly Guo

13. DM Techniques - Logistic Regression • Strengths and weaknesses • Maximum Likelihood Curve Fitting • Multiple Logistic Regression Model • Interaction-effect modifier • Multinomial Logistic Regression Model Guo

14. network architecture with two hidden layers DM Techniques -- Neural Networks • What are Neural Networks • Input layer - a unit for each input variable • Output layer - the target • Hidden layer - hidden unit (neurons) y Guo

15. DM Techniques – Neural Networks • : output activation function. • : activation functions-nonlinear transformations. • : weights • : Bias Guo

16. DM Techniques –Neural Networks • How Neural Networks work • Processing elements • Training • Predicting • Activation Functions • logistic function • hyperbolic tangent Guo

17. DM Techniques -- Neural Networks • Strengths and weaknesses • Accurately prediction for complex problems • Black box predict engine • Overtraining • Training speed Guo

18. DM Techniques -- Hybrid Algorithms • Problems with standard algorithms • Advanced algorithms • Discovery-driven approaches • Mixture of algorithms Guo

19. DM Applications in P&C Insurance • Data Warehouse • Underwriting • Pricing/Rate Making • Claim Scoring • Risk Management • Policy Level Analysis • Variable Selection Guo

20. Primary Selection:WHO? UniquePatient List Transactions Transactions Surveys Surveys Demographics Demographics PharmacyClaims Secondary Selection: WHAT DATA? Rx Service Level Table Derived Variables/ Flags PhysicianClaims Operational Data Store Med Claims Surveys ... Tertiary Selection: WHAT DOES THE TRANSACTION DATA TELL US? Group by Patient HospitalClaims Summary: WHAT DO WE KNOW ABOUT THIS PATIENT? Service Level Variables Summary Level Variables Summary Level Table Data Warehousing Example Guo

21. DM in Insurance Underwriting • Improving profit margin. • Gaining competitive edge • Risk evaluation process. • Lots of variables • Lots of interactions • Easy to follow procedure. • Decision tree can be used Guo

22. DM in Insurance Underwriting - Auto Driver’s Claim Information Guo

23. DM in Insurance Underwriting - Decision Tree Diagram Guo

24. DM in Pricing/Rate Making • Data: Auto Driver’s Claim Information • Decision trees analysis to identify risk factors that predict profits, claims and losses • Logistic regression applied to model • Claim frequency • Effect of each risk factor Guo

25. DM in Pricing/Rate Making Effect T-scores from the logistic regression Guo

26. DM in Pricing/Rate Making - Assessment • Assessment • Cross-model comparisons of the expected to actual profits/losses • Independent of all other factors (sample size,..) • Lift charts • % claim-occurrence value to a random baseline model • Performance quality demonstrated by the degree the lift chart curve pushes upward and to the left Guo

27. DM in Pricing/Rate Making- Lift Chart for Logistic Regression logistic Regression - Captured 30% of the drivers in the 10th percentile - Better predictive power from about the 20th to the 80th percentiles Guo

28. DM in Risk Management • Reinsurance • To structure more effectively by segmentation • Hedging • Target retention and building loyalty Guo

29. DM in Policy Level Analysis • Retention analysis • Profitability analysis • Policyholder’s behavior • DM methods used • Neural networks • Decision trees • Logistic regression Guo

30. Applications – Variable Selection • Problem -- Given {Y,X} where • Find F, such that • Find and F*, such that • Improving model accuracy and efficiency • Making crucial business decisions Guo

31. Case Study - Group Insurance • Identify ways to build upon the current manual rating structure utilizing exiting rating variables to develop a practical tool to guild underwriting in rates adjustments • Identify any new rating variables with significant predictive power • Currently gathered, but not utilized data • Transformations of existing variables • introduce new rating variables (e.g. external financial data) Guo

32. Case Study – Group Insurance • Profit margin over x year period • 128 input variables • Principle Components Analysis applied • 42 variables remains • How to improve business profit? Guo

33. Case Study - Goals • Developing a practical underwriting tool • Detecting deviations • Identifying key drivers • Improving model predictive power • Risk selection Guo

34. Function Approximation • is the initial guess • Stegewise approximation • Each stage added by reducing errors • Each stage is weak linear – a small tree. • Sequential adjustment Guo

35. Regression Tree Example Profit=6.5% +1.2% , if male young than 30 +0.8% , if AS > 421 -1.1% , otherwise -0.5% , otherwise Guo

36. Function Approximation • GIVEN • Y: Output and X: Inputs or Predictors • L(Y, F): Loss Function • ESTIMATE Guo

37. Classical Function Approximation • Solve from Guo

38. Nonparametric Function Approximation • Compute • Initial guess • Take a step in the steepest descent direction Guo

39. Gradient Boosting • Initial guess • FOR m = 1 TO M • Fit an L-node regression tree to the current residuals • For each given node, calculate node average residual • Update: • END Guo

40. Case Study Guo

41. Case Study Guo

42. Case Study- Single Stats and Variable Importance Input Additive Multiplicative Importance Variable 1 0.2679 0.2690 100.00 Variable 2 0.2779 0.3203 75.23 Variable 3 0.1456 0.1771 54.65 Variable 4 0.2263 0.2469 47.41 Variable 5 0.1059 0.1425 42.81 Variable 6 0.2741 0.2847 34.81 Variable 7 0.1289 0.1306 34.27 Variable 8 0.0797 0.0864 25.35 Variable 9 0.1129 0.1148 23.37 Guo

43. Case Study- Pair Stats and Variable Importance VariablesAdditive Multiplicative Variable 1 & Variable 20.3714 0.3847 Variable 2 & Variable30.3704 0.4066 Variable 2 & Variable 40.3686 0.4010 Variable 2 & Variable 7 0.3401 0.3856 Variable 3 & Variable 40.2795 0.3137 Variable 3 & Variable 6 0.2895 0.3082 Variable 4 & Variable 70.2417 0.2592 Variable 5 & Variable 6 0.2622 0.2766 Variable 6 & Variable 70.2904 0.3066 Guo

44. Predictive Modeling • Predicts deviations from expected profitability (used 9 variables) • Practical guide for underwriters to use for rates adjustments • New variables Identified to have strong predictive power • Improve business profit (20% Profit margin) Guo

45. Importance of Multiple Techniques • Robust model with high predictive accuracy • Practical constrains • Algorithm complexity • Ease of understanding of results Guo

46. Is Data Mining for you? • Defining the goals • Understanding your data • Using multiple techniques • Improving your decision making process • Gaining competitive edges! Thank you! Guo