1. P&C Reserve Basic HUIYU ZHANG, Principal Actuary, Goouon Summer 2008, China

2. Where are we Two types of actuaries Life Actuary: Society Of Actuary. Website: http://www.soa.orghttp://www.soa.org Property & Casualty Actuary: Casualty Actuary Society. Web site: http://casact.org One combined organization: American Academy of Actuaries. Web site: http://www.actuary.org/ Actuaries are paid big $$$$, especially P&C Actuary. Here is the information collected by the biggest actuary recuiter DW Simpson http://www.dwsimpson.com/salary

3. P&C Actuary Salary Survey_DW Simpson 09/2007 0-0.5 yrs0.5-2.5-4.5-6.5-9.5-14.5-19.5+ (excl. sign-on)2.5 yrs4.5 yrs6.5 yrs9.5 yrs14.5 yrs*19.5yrs* 1 exam46-6149-6352-68 2 exams47-6354-6756-7361-78 3 exams50-6557-7260-7964-8570-9576-106 4 exams53-6860-7864-8770-9273-10488-129 5 exams 63-8569-9774-10280-11794-140 6 exams 70-8877-10881-11788-124106-161 ACAS 78-10182-11588-130101-149114-183128-251141-268+ 8 exams 85-12295-143106-166127-198 FCAS 111-170123-196143-283150-405158-439+

4. Key functions for insurers Underwriting Claim Actuary Pricing Actuary Reserving Actuary Investment

5. Why reserving is important? The financial condition of an insurance company can not be adequately assessed without sound loss reserve estimates. A loss reserve is a provision for an insurer’s liability for claims. Reserving is the term used to describe the actuarial process of estimating the amount of an insurance company’s liabilities for loss and loss adjustment expenses. It is a challenge for the casualty actuary because the estimation process involves not only complex technical tasks but considerable judgment as well. No formula provides the real answer.

6. Why reserve? To ensure that the company has made “adequate provision” for liabilities associated with all losses, whether reported or not, that were incurred through a specific evaluation date (e.g. 12/31/XX). The liabilities are related to … – The losses themselves, and – The cost of adjusting the losses, that is, loss adjustment expense (LAE).

7. Claim Cycle A. Event occurs B. Insurer is notified of the event C. Insurer gathers facts concerning the event D. Insurer determines whether the event is covered E. Insurer may established a case reserve consistent with the expected ultimate payment F. Insurer may, or may not, issue payment

8. Major Volatility Drivers: Internal Changes in contract language Changes in claim handling process Changes in claim handling staff Changes in claim authorities External Changes in economic conditions Changes in legal environment Changes in inflation Changes in health care

9. Reserving Terms A Case Payment is a payment made by the Claims Dept. on individual claims. A Case Reserve is a liability established by the Claims Depart. on an individual claim. A Case Incurred Loss is the sum of all case payments and case reserves.

10. Reserve Terms_Continue Incurred But Not Reported (IBNR) is the additional reserves that a company must carry such that the sum of the case reserves and the IBNR makes “adequate provision” for liabilities associated with all losses that were incurred through a specific evaluation date. IBNR includes amounts for… – Development on reported claims, and – Unreported claims that have been incurred through the valuation date.

11. Standard Methods of Property – Casualty Loss Development Analysis : Incurred Loss Development Paid Loss Development Numerous other methods of increasing analytic sophistication

12. Paid Loss Development Assumes past patterns of changes in paid losses from one period to the next are on average predictive of future changes in paid losses. Assumes case reserves are not meaningful.

13. Incurred Loss Development Assumes past patterns of changes in the incurred losses from one period to the next are on average predictive of future changes in incurred losses. Assumes paid dollars and case reserves are equally meaningful.

14. Incurred Loss Development Paid & Case Incurred Losses 1224364860 20011,0001,2001,3201,3901,380 20021,1001,3201,4501,520 20031,2101,4501,600 20041,3301,600 20051,460

15. Age to Age Factors 12-2424-3636-4848-60 2001120%110%105%99% 2002120%110%105% 2003120%110% 2004120% Ave.120%110%105%99% 0% 20% 40% 60% 80% 100% 120% 140% 2001200220032004 12-2424-3636-4848-60 Incurred Age to Age Factors

16. Paid Losses 1224364860 20012006009901,2511,380 20022206601,0881,368 20032427251,200 2004266800 2005292 Paid Loss Development

17. Age to Age Factors 12-2424-3636-4848-60 2001300%165%126%110% 2002300%165%126% 2003300%166% 2004301% Ave.300%165%126%110% 0% 50% 100% 150% 200% 250% 300% 350% 2001200220032004 12-2424-3636-4848-60 Paid Age to Age Factors

18. Projection of Ultimate Paid Losses 1224364860 20012006009901,2511,380 20022206601,0881,368 1,509 20032427251,200 1,5131,669 2004266800 1,3211,6651,837 2005292 8761,4471,8242,012 Ultimate Paid Losses

19. Case Reserved Losses 1224364860 20018006003301390 2002880660362152 2003968725400 20041,064800 20051,168 0 200 400 600 800 1,000 1,200 1,400 1224364860 20012002200320042005 Case Reserve Development

20. Ratio of Current Case to Prior Case 24364860 200175%55%42%0% 200275%55%42% 200375%55% 200475% Ave.75%55%42%0% 10% 20% 30% 40% 50% 60% 70% 80% 2001200220032004 24364860 Case Age to Age Factors

21. Projection of Case Reserves 1224364860 20018006003301390 2002880660362152 0 2003968725400 1680 20041,064800 4401850 20051,168 8764822030 Ultimate Case Reserves

22. Paid Losses 1224364860 20012006009901,2511,380 20022206601,0881,368 20032427251,200 2004266800 2005292 Paid Loss Development

23. Change In Paid 24364860 2001400390261129 2002440428280 2003483475 2004534 0 100 200 300 400 500 600 24364860 2001200220032004 Change In Paid

24. Ratio of Change In Paid to Prior Case 24364860 200150%65%79%93% 200250%65%77% 200350%66% 200450% Ave.50%65%78%93% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 24364860 2001200220032004 Ratio of Change in Paid to Prior Case

25. Paid Projection 1224364860 20012006009901,2511,380 20022206601,0881,368 1,509 20032427251,200 1,5131,669 2004266800 1,3211,6651,837 2005292 8761,4471,8242,012 Ultimate Paid Loss Projection

26. Why Age, why triangle People Comparison AY Loss Comparison Past trend for same age group could be used to analyze future unknown _People _Loss

27. How to age Examples: HowToAgeData1 HowToAgeData2 End of appetizer, next, main dish.

28. Paper Introduction Blame received for reserving actuary 2003 S&P #1 CAS Story Caveat of link ratio Simplest Liner Relationship Go to paper Triangle 1 and Triangle 2

29. Reserve Variability Estimates Parameter Risk, Process Risk, Model Risk and other risks. Two approaches Bootstrap_ Parameter Risks Simulating LDF_ Process Risks 2 Stage Bootstrap_ Parameter and Process Risks

30. 2 Stage Bootstrap Bootstrap: Resample with replacement, “new” generation of simulation. Resample residuals. Residuals are generally iid. What is the residual? Pearson residuals (good for Poisson GLMs): (A-E)/E^0.5

31. How to get residual Triangle 3: residuals Triangle 4: A- Actual Payments (incremental) Triangle 5: E- Expected Payments (incremental)

32. Bootstrap and Pseudo triangles Triangle 7: Resampled Residuals Compare with triangle 3 Triangle 8: Pseudo triangles Repeat End of First Stage Explain Results: Table 2

33. Stage 2: resolve process risk Interrupt First Stage Mean, variance, distribution Appendix: triangle 9, triangle 10 Explain Result: table 4. End of main dish. Next: Dessert