Credible Risk Classification

1. Credible Risk Classification CAS Ratemaking Journal 2004 Written by Ben Turner of Farmers Insurance

2. Skim the Cream vs. Adverse Selection

3. Segmentation As book is sliced indications become erratic, unreliable, and disrupting to policyholders. Hence actuaries opt to credibility weight

4. Roadmap

5. A Simple Example

6. A Simple Example—Alternate Class Plan

7. Potential Groupings of Four Levels

8. Segmentation vs. Credibility

9. Segmentation vs. Credibility

10. Simulation

11. Simulation Results

12. Simulation Results

13. Roadmap

14. A Simple Example

15. “Losses Squared” • For EACH POLICY the losses are squared and then divided by the exposures of that policy. • The results can then be summed up and the underlying detail does not need to be maintained. • This allows the computation of variance without having to keep policy level detail.

16. A Simple Example

17. Calculation of Credibility Buhlmann-Empirical-Bayes • It assumes no underlying distribution. • It is relatively uncontroversial. • It supplies its own complement of credibility. • It does not require arbitrary selection of parameters. See Loss Models, Klugman, et. al.

18. Calculation of Credibility Required Calculations • V = Process Variance • A = Variance of Hypothetical Means • K = V/A • Credibility = Exposures / (Exposures + K)

19. Calculation of Credibility Calculation of V, the Process Variance

20. Calculation of Credibility Calculation of A, the Variance of the Hypothetical Means

21. Calculation of Credibility Calculation of K and Credibility • K = V/A • Credibility = Exposures / (Exposures + K)

22. Calculation of Credibility

23. Credibility-Weighted Class Mean

24. Calculation of Score

25. Score: Calculation of Numerator

26. Score: Calculation of Denominator Denominator = 66,977,631,413-5,430,959,280 = 61,546,672,133

27. Calculation of Score

28. Segmentation vs. Credibility

29. A Simple Example—Alternate Class Plan

30. Segmentation vs. Credibility

31. Roadmap

32. Score’s Factors An increase in any of the following, will raise Score, ceterus paribus: • The difference between the class means • The credibility of each class • The number of classes

33. Calculation of Score Factors: 1) Difference between means, 2) Credibility, 3) Number of Classes

34. Segmentation vs. Credibility

35. Score’s Theory Score is theoretically correct because it: • Will tend to occur inadvertently via the free markets • Is designed explicitly for this actuarial issue • Uses the correct standard of proof

36. Roadmap

37. Complex Hypothetical Example Company introduced specialty line and tracked: • Location • Radius of operation • Whether the business is owner-operated It now seeks to create a class plan, and is willing to have the plan be nonlinear.

38. A Sample from the Database

39. Summarized Data

40. 2,048 Potential Class Plans

41. Selected Class Plan

42. Underwriting Guidelines

43. Roadmap

44. Complex Example—Linear Class Plan

45. Complex Example—Linear Class Plan—Alternate A

46. Complex Example—Linear Class Plan—Alternate B

47. Roadmap

48. Conclusion We’ve seen: • Score is a theoretically correct method • Score can be done in a spreadsheet • Score can be iterated over all possible plans via a computer program • Score can be used on just the class plans that are of interest • Score can help you design superior class plans