1. General Insurance Spring Seminar Friday 21 May 2004, Staple Inn Hall

2. Reserve Ranges & Stochastic Reserving  1. Background  2. Thomas Mack Method  3. Multi-Line  4. Alternative “Practical” Approach

3. Ranges in Practice  Percentages  Varying Parameters  Stochastic

4. Stochastic Methods: Problems  To match deterministic model  BF methodology  Incurred claims: redundancy  Spurious data  Tail  Multi-lines/correlation  Large losses  Latent claims

5. Stochastic v Deterministic Not same mid-point:  Use range unchanged  Move range  Pro-rata adjustment

6. Thomas Mack Method Assumptions:  Independence of accident years  E(C i,k+1 |C i1,…C ik ) = C ik f k  Var(C i,k+1 |C i1,…C ik ) = C ik  k 2

7. Mack Adjustments  Alternative development factors  Omit data cells  By year to give correct overall result  BF  Tail

8. Formulae  Standard error by accident year given by:

9. Formulae: last s.e.  Given by:

10. Formula: Overall Standard Error  Standard error overall and adjustment given by:

11. Formula: Tail Factor Adjustment  Tail factor adjustment given by:

12. BF A Priori Loss Ratio Variability Choices:  Time Series  Rate/Inflation Adjusted

13. BF as Credibility Formula Formula for standard error: 

14. Multi-Line  Correlation between classes  Use @Risk and Correlation Matrix  Paper gives simple alternative: basic copula

15. Chain-Ladder Practical Alternative  Follow deterministic method  Standard errors based on selected/alternative development factors  Use @Risk to complete triangle  Allow for correlation where appropriate  Part-year triangles/large losses/omit cells etc.  BF adjustment as above

16. Graph of Results