Tail Factors Working Party: Part 2. The Work Product Mark R. Shapland, FCAS, ASA, MAAA Casualty Loss Reserve Seminar Boston, MA September 12-13, 2005

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

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

Bondy-Type Methods 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 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

Algebraic Methods 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 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

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

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

Open Claim Methods 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

Curve Fitting Methods 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 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

Lifespan Methods 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 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

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

Miscellaneous Methods 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