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

2. Finite Reinsurance Reserving 2 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 3 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 4 Aggregate XOL Retention = 75% l/r or $750M LAYER OF COVERAGE Limit + Retention = 85% l/r or $850M Retained Losses

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

6. Finite Reinsurance Reserving 6 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 7 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 8 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 9 Credit Risk – Interest Income Current Interest %Credit Risk* 2%$16 M 3%$13 M 4%$9 M 5%$6 M 6%$4 M 7%$1 M 8%0 8.5%0 * PV of Shortfall if FWB is transferred to Reinsurer and only earns Current Interest %.

10. Finite Reinsurance Reserving 10 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 11 Credit Risk – Under-Reporting Current Interest % Credit Risk w/o Offset on Future APs Credit Risk with Offset on Future APs 2%$54 M$27 M 3%$51 M$23 M 4%$48 M$20 M 5%$45 M$17 M 6%$42 M$14 M 7%$39 M$12 M 8%$37 M$9 M 8.5%$36 M$8 M * PV of Shortfall if FWB is transferred to Reinsurer and only earns Current Interest %.

12. Finite Reinsurance Reserving 12 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 13 Amount of APs Payment DateAP with Interest 200055% 200160% 200265% 200370% 200476% 200583% 200690% 200797% 2008106%

14. Finite Reinsurance Reserving 14 Tail Factor Selection

15. Finite Reinsurance Reserving 15 Tail Factor Selection Tail FactorFWB Cushion* 1.000- $2.4 M 1.005- $0.7 M 1.010$0.6 M 1.015$1.4 M 1.020$2.2 M * Negative Numbers are PV Reinsurers Loss at 4%.

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