1. Claims Reserving for Non Life Insurance Craig Thorburn, B.Ec., F.I.A.A. Cthorburn@worldbank.org Phone +1 202 473 4932

2. Agenda The objectives of loss reserving Techniques The role of the supervisor Illustrative examples

3. Objectives of Loss Reserving The statistical basis of insurance Supervisory objectives Company objectives

4. The Statistical Basis of Insurance

5. The Risk of Ruin Taking account of –Expected and unexpected events –Expected and unexpected outcomes of size of claims –Expected and unexpected timing issues –The potential for misestimating values What is the chance that we will not have enough funds to meet our obligations? Do we have enough resources to cover the potential adversity in outcome?

6. At an acceptably small probability of being wrong Total Claims Cost Point where claims use up available resources Probability of Exceeding “Ruin”

7. Supervisory Objectives Adequacy Normally, assessment on a “not less than reasonable” basis Value relates to determining excess assets Value can relate to determining solvency margin requirements

8. Company Objectives Economic capital requirements Other external pressures –Ratings agencies –Solvency breach minimisation Profit smoothing Taxation management Management remuneration schemes

9. Small Numbers and Large Numbers On the balance sheet numbers are small On the P&L numbers are large For example –Company seeks profit of 3% of premiums –Investment earnings are 10% pa –Business is long tail (term 4 years) –2% increase in provisioning will eliminate the year’s profit

10. Agenda The objectives of loss reserving Techniques The role of the supervisor Illustrative examples

11. Techniques Case estimates Run-off methods Stochastic methods Advantages and disadvantages Issues –Establishing assumptions –Reinsurance allowance –Quality of data

12. Case Estimates Each claim has a file opened when it is notified Estimates are made, and updated, as information comes to hand Payments made are recorded against the file When the claim is finalised, the file is closed

13. Run-off Methods Use models to complete the future expected payments Several methods are available Assume past (observed) processes continue into the future

14. Stochastic Methods Full models of claims size and delay are established Can be enhanced by simulation methods Provide a great deal of information about the range of answers – not just one answer

15. Advantages and Disadvantages Case estimates do not include IBNR Case estimates use all available information about a claim Case estimates can be biased by management attitudes Case estimates are easy to implement Run-off and Stochastic methods rely on stability of procedures and quality of data Run-off and Stochastic methods are more difficult to implement and to interpret

16. Issues Establishing Assumptions Reinsurance allowance Quality of data

17. Questions and comments

19. Agenda The objectives of loss reserving Techniques The role of the supervisor Illustrative Examples

20. The role of the supervisor What can you do? –Ratio analysis –Runoff methods –Back-testing Case Estimates –Use of Actuaries –On Site Inspections

21. Ratio Analysis Collect data on the numbers of claims, case estimates, and amounts of claims to date and expected by business line and accident year. Compare company to company and period to period looking for extremes and sudden changes.

22. Runoff Methods Can be applied to data submitted to check answers for reasonableness Ideally, several methods would be used

23. Back-testing Case Estimates Important to see how adequate they have been. Compare last year’s case estimates with this year plus claims paid less allowance for investment income and expenses. Similar to case estimate development method (covered later).

24. Use of Actuaries Interview actuaries who have done evaluations. Read existing actuarial reports. Compare actuarial methods and assumptions. Seek an independent actuarial report. Employ internal actuaries in the supervisor.

25. On Site Inspections Activity will depend on time taken and assessed risk –Examine actuarial data sources –Examine actuarial processes –Review assumptions

26. Agenda The objectives of loss reserving Techniques The role of the supervisor Illustrative example

27. Illustrations Chain ladder method –Based on CUMULATIVE data –Can do numbers or amounts of claims incurred or paid or case estimates

28. The Starting Point

29. Historic data Past numbers of claims for each year It is important to have quality data which is homogeneous Separate business lines and categories

30. The Objective Past numbers of claims for each year Filling in the gap…

31. Step 1: Make the Table Cumulative

32. Step 2: Calculate Ratios

33. Step 3: Apply Ratios to Project Figures

34. Actual Data I used…

35. Comparison of Results

36. 150 cases using average ratio 45% proved, in hindsight, to be adequate

37. 150 cases using worst observed ratio 92% proved, in hindsight, to be adequate

38. Questions and comments