2. Reserving for Medical Professional Liability Casualty Loss Reserve Seminar September 10-11, 2001 New Orleans, Louisiana Rajesh Sahasrabuddhe, FCAS, MAAA Aon Risk Consultants, Inc.

3. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 2 Presentation of Model  Motivation & Rationale  Theory via Case Study Mid level discussion with technical references  Questions and Answers

4. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 3 Motivation & Rationale  Zehnwirth / Barnett “The standard link ratio models carry assumptions not usually satisfied by the data” Why?  SIR’s on Occurrence Basis / Excess is often on a Claims-Made Basis

5. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 4 Motivation & Rationale  A model easily adaptable to simulation techniques  A Model that works with client data Many clients do not track triangles; they simply have a loss run

6. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 5 Our Experience with Reserving for HPL  IBNER is generally minimal Case reserves, in the aggregate, tend to be reasonably adequate Most Healthcare institutions are conservative by nature  The majority of cost stems from suits The rest is just noise  Simulation is necessary To model alternative coverage programs To determine variability in results

7. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 6 Reserve Analysis  IBNR Liabilities are the sum of the following Incurred but not enough reported (“IBNER”) True Incurred but not reported  Estimate Components Separately

8. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 7 Timeline for Case Study Mar 31, 2001Oct 1, 2001Sep 30, 2002 Reserve Analysis – All events occurring SIR Loss Forecast – All events occurring Excess Insurance – All events reported

9. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 8 IBNER  IBNER may be estimated using: Case reserve adequacy statistics for the insurance industry – claims made coverage triangles from A.M. Best Payment model – large clients “Last Reserve” statistics  Factors of IBNER / Reported Loss are simulated Dew and Hedges – Reserving for Excess Layers

10. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 9 True IBNR the interesting part  True IBNR is estimated using a frequency x severity approach  Why? - This model is the most consistent with the real world!

11. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 10 Our Reserve Analysis: True IBNR Frequency  IBNR Frequency is a direct function of exposure, initial expected ultimate frequency and report lag - i.e. IBNR frequency should be estimated using a B-F approach  Critical Assumption – How long between accident occurrence and claim reporting – Use approach contained in Weissner – “Estimation of the Distribution of Report Lags by the Method of Maximum Likelihood” - Proceedings of the Casualty Actuarial Society (1978)

12. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 11 Report Lag  The lag experience is truncated from above  Similar to a deductible problem (Hogg & Klugman)

13. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 12 Report Lag  Use Maximum Likelihood Techniques (“ Loss Models” – KPW)  Use a B-F model

14. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 13 True IBNR Frequency  Use pattern to allocate to claims-made periods  May also apply model to estimate lag between report and closing  Frequency is simulated as a Poisson distribution

15. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 14 True IBNR Severity  Severity Model Closed w/ Indemnity? Yes No Exp. Only Model Indemnity Model

16. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 15 True IBNR Severity  Fit severity models using individual claim data  Myriad of references for estimating claim severity distributions. My personal suggestions are: Klugman, Panjer, & Wilmot - Loss Models Keatinge – Modeling Losses with the Mixed Exponential Distribution

17. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 16 Loss Forecast and Excess Insurance Analysis  Through our True IBNR reserve analysis, we have already developed the parameters necessary for: the loss forecast and the excess insurance analysis!  So we simply extend to the prospective year; but separately capture the results

18. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 17 Simulation (Part 1)  Model the entire claims process

19. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 18 Simulation (Part 2)  Model the entire claims process

20. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 19 Result  A model that is both flexible and robust  A model that makes sense – ties with the real world  A model that provides results of interest to clients

21. Casualty Loss Reserve Seminar September 10-11, 2001 Slide 20 Other considerations / future enhancements  “Basic losses” / “Shock Losses”  Model severity as a function of the report lag  Separate severity distributions for lawsuits and claims  Parameter Risk