Finite Reinsurance Reserving

1. Finite Reinsurance Reserving Nick Giuntini, FCAS, MAAA CLRS, September 2003

2. Finite Reinsurance Reserving General Approach • Generally Reserved on an Individual Contract Basis • Lack of Homogeneity • LPTs, Agg XOLs, Q/Ss • Varied Terms • Varied Underlying • Often Large Contracts • Underlying Exposure and Deal Modeling • Accounting May Vary • Risk Transfer – Reinsurance Accounting • Can Reinsurer Discount Reserves? • “No Risk Transfer” – Deposit Accounting

3. Finite Reinsurance Reserving Hypothetical Aggregate XOL • Whole Account • $1 Billion Est. Subject Premium • 10% xs 75% Loss Ratio or $100M xs $750M of Losses • Additional Premium = 55% of Covered Loss • Funds Withheld Balance (FWB) • Crediting Interest Rate = 8.5% • Effective 1/1/2000 (2000 Underwriting Year)

4. Finite Reinsurance Reserving Aggregate XOL Retained Losses LAYER OF COVERAGE Limit + Retention = 85% l/r or $850M Retention = 75% l/r or $750M Retained Losses

5. Finite Reinsurance Reserving Aggregate XOL FWB Limit = $100M INTEREST CREDIT COVERED LOSSES Premium = $55M

6. Finite Reinsurance Reserving Mean or Mode • Assume: • Reinsurer can Discount Losses • Cedent Reports a 80% loss ratio • FWB Expected to Cover Ceded Loss Payout ($27.5M of Premium + Interest for $50M Losses) • Should Reinsurer Set up a Reserve for Obligations in Excess of FWB?

7. Finite Reinsurance Reserving Credit Risk • If Cedent becomes Insolvent, Reinsurer’s Funds are at Risk: • Premiums and Interest “Paid” into FWB • Funds Transferred Triggers on Certain Events • If not transferred offset generally believed to hold • Premiums not yet Paid into FWB • Offset Probably Holds • Future Interest Credits • Offset Questionable

8. Finite Reinsurance Reserving Credit Risk – Interest Income • Assume: • Reserving at 12/31/2003 • Expected Loss Ratio = 85% • $736M Paid to Date (Paid Losses still in Retention) • FWB = $76M (for $100M of Ceded Losses) • What is the Magnitude of the Reinsurer’s Credit Risk?

9. Finite Reinsurance Reserving Credit Risk – Interest Income * PV of Shortfall if FWB is transferred to Reinsurer and only earns Current Interest %.

10. Finite Reinsurance Reserving Credit Risk – Under-Reporting • Assume: • Same as before, but • Expected Loss Ratio = 85%, • Reported Loss Ratio = 80% • FWB = $38M (for $50M of Reported but ultimately $100M of Reported Losses) • Now What is the Magnitude of the Reinsurer’s Credit Risk?

11. Finite Reinsurance Reserving Credit Risk – Under-Reporting * PV of Shortfall if FWB is transferred to Reinsurer and only earns Current Interest %.

12. Finite Reinsurance Reserving Tail Factor Selection • Generally Higher Tail Factors are “Conservative” for the Reinsurer • For this Cover, an Increase in Paid Losses After 8 Years is Good for Reinsurer • Assume: • Reserving at 12/31/2003 • Expected Loss Ratio = 80% (given tail factor) • $694M Paid to Date (Paid Losses still in Retention)

13. Finite Reinsurance Reserving Amount of APs

14. Finite Reinsurance Reserving Tail Factor Selection

15. Finite Reinsurance Reserving Tail Factor Selection * Negative Numbers are PV Reinsurers Loss at 4%.

16. Finite Reinsurance Reserving Conclusion • There can be Additional Reserving Issues and Concerns for Finite Contracts Due to: • Contract Structure • Legal Jurisdiction • Accounting Regime