1. Loss Reserve Variability Using DFA Approaches Casualty Loss Reserve Seminar September 19, 2000 Minneapolis

2. Loss Reserves in DFA Speakers –Chuck Emma, Paratus Consulting Limited Basic reserve modeling for unanticipated inflation –Susan Witcraft, Milliman & Robertson Modeling non-inflation variability –Nylesh Shah, PriceWaterhouse Coopers, LLP Reserve risk factor analysis

3. Basic Reserve Modeling Overview General Concepts Basic Illustration of Reserve Variability –Randomness in future loss payouts –Unanticipated inflation

4. Basic Reserve Modeling General Concepts Which reserve elements to model? –payment dollars –payout percentages Which risk factors to model? –economic inflation –social inflation –extra-normal shifts Best Estimates vs. Recorded Reserves

5. Basic Reserve Modeling General Concepts (cont’d) Which results to measure? Validation Metrics Dependency (correlation) with inflation Autocorrelation across accident years Autocorrelation across payment lags Performance Metrics Schedule P development Future calendar year impact Future surplus position

6. Basic Reserve Modeling Illustration Notion Future loss payments (reserves) vary, relative to a-priori expectations, due to two drivers: Unexpected inflation Pure randomness Loss Reserve Development = (A-Priori Loss Payments) – (Generated Loss Payments)

7. Basic Reserve Modeling Illustration (cont’d) Single Accident Year (2000) - Example 200020012002200320042005Total Expected Payout 500200100 50 1,000 Generated Payout 51025011015080601,160 Ultimates over time 1,0101,0601,0701,1201,1501,160

8. Basic Reserve Modeling Illustration (cont’d) Overall Modeling Process Step 1: Parameterize (by Line) A. Estimate mean and variability of loss payout patterns percentages (piecewise) B. Define expected loss reserve inflation factor (adequacy parameter), say 6.0%.

9. Basic Reserve Modeling Illustration (cont’d) Step 1 (cont’d) Expected Reserve Payout Pattern Accident Year 200020012002200320042005Total 1995 100.0% 1996 50.0 100.0 1997 50.025.0 100.0 1998 33.3 16.7 100.0 1999 40.020.0 10.0 100.0 2000 50.020.010.0 5.0 100.0

10. Basic Reserve Modeling Illustration (cont’d) Step 1 (cont’d) Resultant A-Priori (Static) Reserve Schedule Accident Year 20002001200220032004ReserveUltimate 1995 50 1,000 1996 52531051,050 1997 11055 2201,100 1998 115 57583451,150 1999 240120 60 6001,200 Total 568343233118601,3205,500

11. Basic Reserve Modeling Illustration (cont’d) Step 2: Generate Stochastic Inflation Path Calendar Year Generated Inflation Inflation Index Normal Index Inflation Adjustment Factor 2000 6.5%1.065 1.060 1.005 2001 6.8%1.1371.124 1.012 2002 7.2%1.2191.191 1.024 2003 7.6%1.3121.262 1.039 2004 7.8%1.4141.338 1.057

12. Basic Reserve Modeling Illustration (cont’d) Step 3: Generate Payout Percentages Payment Year A-PrioriGenerated 150.0%40.0% 220.0%15.0% 310.0%15.0% 410.0% 55.0%10.0% 65.0%10.0% A-Priori Generated

13. Basic Reserve Modeling Illustration (cont’d) Step 3 (cont’d) Generated Reserve Payout Pattern Accident Year 200020012002200320042005Total 1995 100.0% 1996 50.0 100.0 1997 50.025.0 100.0 1998 33.322.2 100.0 1999 25.0 16.7 100.0 2000 40.015.0 10.0 100.0

14. Basic Reserve Modeling Illustration (cont’d) Step 4: Combine the two to calculate future loss payments (for accident years 1995-1999) Calendar Year 20002001200220032004Total Scheduled Payout 568343233118601,320 Varied Payout 4413532501771001,320 Inflation Adj. 1.0051.0121.0241.0391.057 Modeled Payout 4433572561841061,345 (4.9%)

15. Basic Reserve Modeling Other Thoughts What if Costs Shift Suddenly? –Mass tort emergence –Expanded liability –Tort reform Some Ideas –Stochastic shocks to inflation modeling –Varying payouts over relevant accident year –Individual policy modeling (limit stacking)