Paper Overview

1. Tail Factors Working Party:Part 2. The Work Product Mark R. Shapland, FCAS, ASA, MAAACasualty Loss Reserve SeminarBoston, MASeptember 12-13, 2005

2. Organized by “Type” of Method Sections Describe: Mechanics of each method, Examples for most methods, Results of our Testing, and Results of our Surveys Paper Overview

3. Standard Notation: Consistency, Started with Notation from Reserve Variability Working Party Added new notation where lacking Summarize Areas for Future Research Paper Overview

4. Bondy-Type Methods Algebraic Methods Benchmark Methods Open Claim Methods Curve Fitting Methods Lifespan Methods Miscellaneous Methods Section Overview

5. Bondy Method Use last link ratio: Modified Bondy Method Double or square: Generalized Bondy Method (Weller) For 0<B<1: Fully Generalized Bondy Method (Gile) Let Vary by Accident Year Bondy-Type Methods

6. Advantages Simple to Implement Pattern Described with One Factor Only Requires Cumulative Paid Data Disadvantages Not Always Useful for Incurred Data Will Fail with Increasing Development May Fail with “More Complicated” Patterns Bondy-Type Methods

7. Equalizing Paid & Incurred Loss Estimates Use Cumulative Incurred / Cumulative Paid Boor’s Method Adjust Case Reserves Mueller’s Method Adjust Incremental Factors NCCI Method Algebraic Methods

8. Advantages Simple to Implement Only Requires Cumulative Data Statistically Unbiased Disadvantages May Not be Sophisticated Enough Subject to Case Reserve Distortions Some Methods Not Generally Well Known Algebraic Methods

9. Benchmark Development / Link Ratios Adjusted Benchmark Development / Link Ratios Use Link Ratios to Adjust Tail Factor Benchmark Average Severity Benchmark Adjusted by Claims Audit Benchmark Methods

10. Advantages: Supplement when Little Data Adds Credibility Various Degrees of Sophistication Disadvantages: Need Similar Data Claim Handling Procedures Relative Case Reserve Strength Benchmark Methods

11. Maximum Possible Loss Judgment of Open Claim Costs / Audit Open Claim Methods

12. Advantages: Incorporates Particulars of Open Claims Uses Knowledge of Claim Staff Can Provide Bounds Disadvantages: Requires Access to Individual Claims Subject to Judgment/Availability of Auditors May Underestimate for Severe Cases Open Claim Methods

13. Exponential Decay Constant Rate of Factor Decay McClenahan’s Method Constant Monthly Incremental Paid Decay Skurnick’s Method Simplify Using Annual Decay Sherman’s Method Use “Inverse Power” Curves England-Verrall Method Smooth & Extrapolate Incremental Data Curve Fitting Methods

14. Advantages: Straightforward & Intuitive Extrapolate Beyond End of Data Various Levels of Sophistication Disadvantages: May Underestimate Tail for Long-Tail Lines Sub-Optimal If Pattern Not Consistent Sometimes No Closed Form Solution Curve Fitting Methods

15. Static Mortality Method Frequency / Severity Using Mortality Rates Trended Mortality Method Greatest Impact on “Distant” Years Sherman-Diss Method Separate Impact of Inflation & Mortality Corro’s Method Modeling of “Pension” Claims Lifespan Methods

16. Advantages: Extrapolate “Very-Long” Tail Can Include “Increasing” Factors Detailed Assumptions/Some Non-Subjective Disadvantages: More Complex Need “Very Old” Data to Parameterize Need Specific Mortality Rates Lifespan Methods

17. Restating Historical Experience via a Claims Audit Adjust for Changes Miscellaneous Methods

18. Advantages: Improves “Other” Methods Adjustments Readily Understood Add Claim Professional Judgment Disadvantages: Difficult to Reconstruct Old Claim Files Auditor Must Ignore Prior Development Auditor Must Evaluate at Multiple Points Miscellaneous Methods