Reserving for Medical Professional Liability

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

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

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 Casualty Loss Reserve Seminar September 10-11, 2001

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 Casualty Loss Reserve Seminar September 10-11, 2001

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 Casualty Loss Reserve Seminar September 10-11, 2001

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 Casualty Loss Reserve Seminar September 10-11, 2001

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

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 Casualty Loss Reserve Seminar September 10-11, 2001

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

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) Casualty Loss Reserve Seminar September 10-11, 2001

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

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

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 Casualty Loss Reserve Seminar September 10-11, 2001

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

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 Casualty Loss Reserve Seminar September 10-11, 2001

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 Casualty Loss Reserve Seminar September 10-11, 2001

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

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

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 Casualty Loss Reserve Seminar September 10-11, 2001

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 Casualty Loss Reserve Seminar September 10-11, 2001