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P&C Reserve Basic HUIYU ZHANG, Principal Actuary, Goouon Summer 2008, China Where are we Two types of actuaries Life Actuary: Society Of Actuary. Website: http://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 P&C Actuary Salary Survey_DW Simpson 09/2007 0-0.5 yrs 0.5- 2.5- 4.5- 6.5- 9.5- 14.5- 19.5+ (excl. sign-on) 2.5 yrs 4.5 yrs 6.5 yrs 9.5 yrs 14.5 yrs* 19.5 yrs* yrs* 1 exam 46-61 49-63 52-68 2 exams 47-63 54-67 56-73 61-78 3 exams 50-65 57-72 60-79 64-85 70-95 76-106 4 exams 53-68 60-78 64-87 70-92 73-104 88-129 5 exams 63-85 69-97 74-102 80-117 94-140 6 exams 70-88 77-108 81-117 88-124 106-161 ACAS 78-101 82-115 88-130 101-149 114-183 85-122 95-143 106-166 127-198 111-170 123-196 143-283 8 exams FCAS 128-251 141-268+ 150-405 158-439+ Key functions for insurers Underwriting Claim Actuary Pricing Actuary Reserving Actuary Investment 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. 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). Claim Cycle A. B. C. D. E. F. Event occurs Insurer is notified of the event Insurer gathers facts concerning the event Insurer determines whether the event is covered Insurer may established a case reserve consistent with the expected ultimate payment Insurer may, or may not, issue payment 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 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. 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. Standard Methods of Property – Casualty Loss Development Analysis Incurred Loss Development Paid Loss Development Numerous other methods of increasing analytic sophistication : 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. 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. Incurred Loss Development 1,800 1,600 1,400 1,200 1,000 800 600 400 200 0 12 24 2001 Paid & Case Incurred Losses 12 24 2001 1,000 1,200 2002 1,100 1,320 2003 1,210 1,450 2004 1,330 1,600 2005 1,460 36 1,320 1,450 1,600 36 2002 48 1,390 1,520 48 2003 60 1,380 2004 2005 60 Incurred Age to Age Factors 140% 120% 100% 80% 60% 40% 20% 0% 2001 2002 2003 12-24 24-36 36-48 Age to Age Factors 2001 2002 2003 2004 Ave. 12-24 120% 120% 120% 120% 120% 24-36 110% 110% 110% 36-48 105% 105% 48-60 99% 110% 105% 99% 2004 48-60 Paid Loss Development 1,600 1,400 1,200 1,000 800 600 400 200 0 12 24 36 2001 2002 2003 48 2004 Paid Losses 2001 2002 2003 2004 2005 12 200 220 242 266 292 24 600 660 725 800 36 990 1,088 1,200 48 1,251 1,368 60 1,380 60 2005 Paid Age to Age Factors 350% 300% 250% 200% 150% 100% 50% 0% 2001 2002 12-24 Age to Age Factors 12-24 2001 300% 2002 300% 2003 300% 2004 301% Ave. 300% 2003 24-36 24-36 165% 165% 166% 36-48 126% 126% 48-60 110% 165% 126% 110% 36-48 2004 48-60 Ultimate Paid Losses 2,500 2,000 1,500 1,000 500 0 12 24 36 2001 Projection of Ultimate Paid Losses 12 2001 200 2002 220 2003 242 2004 266 2005 292 24 600 660 725 800 876 36 990 1,088 1,200 1,321 1,447 2002 2003 48 1,251 1,368 1,513 1,665 1,824 48 2004 60 1,380 1,509 1,669 1,837 2,012 60 2005 Case Reserve Development 1,400 1,200 1,000 800 600 400 200 0 12 24 36 2001 Case Reserved Losses 12 2001 800 2002 880 2003 968 2004 1,064 2005 1,168 24 600 660 725 800 2002 36 330 362 400 2003 48 139 152 48 2004 60 0 60 2005 Case Age to Age Factors 80% 70% 60% 50% 40% 30% 20% 10% 0% 2001 2002 2003 24 36 48 60 Ratio of Current Case to Prior Case 2001 2002 2003 2004 Ave. 24 75% 75% 75% 75% 75% 36 55% 55% 55% 48 42% 42% 60 0% 55% 42% 0% 2004 Ultimate Case Reserves 1,400 1,200 1,000 800 600 400 200 0 12 24 36 2001 Projection of Case Reserves 12 2001 800 2002 880 2003 968 2004 1,064 2005 1,168 24 600 660 725 800 876 36 330 362 400 440 482 2002 48 2003 48 139 152 168 185 203 2004 60 0 0 0 0 0 60 2005 Paid Loss Development 1,600 1,400 1,200 1,000 800 600 400 200 0 12 24 36 2001 2002 2003 48 2004 Paid Losses 2001 2002 2003 2004 2005 12 200 220 242 266 292 24 600 660 725 800 36 990 1,088 1,200 48 1,251 1,368 60 1,380 60 2005 Change In Paid 600 500 400 300 200 100 0 24 36 2001 48 2002 2003 2004 Change In Paid 2001 2002 2003 2004 24 400 440 483 534 36 390 428 475 48 261 280 60 60 129 Ratio of Change in Paid to Prior Case 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 24 36 2001 48 2002 2003 60 2004 Ratio of Change In Paid to Prior Case 2001 2002 2003 2004 Ave. 24 50% 50% 50% 50% 50% 36 65% 65% 66% 48 79% 77% 60 93% 65% 78% 93% Ultimate Paid Loss Projection 2,500 2,000 1,500 1,000 500 0 12 24 36 2001 2002 2003 48 2004 Paid Projection 2001 2002 2003 2004 2005 12 200 220 242 266 292 24 600 660 725 800 876 36 990 1,088 1,200 1,321 1,447 48 1,251 1,368 1,513 1,665 1,824 60 1,380 1,509 1,669 1,837 2,012 60 2005 Why Age, why triangle People Comparison AY Loss Comparison Past trend for same age group could be used to analyze future unknown _People _Loss How to age Examples: HowToAgeData1 HowToAgeData2 End of appetizer, next, main dish. 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 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 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 How to get residual Triangle 3: residuals Triangle 4: A- Actual Payments (incremental) Triangle 5: E- Expected Payments (incremental) 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 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