Tail Factors Working Party:

Part 2. The Work Product

Mark R. Shapland, FCAS, ASA, MAAA

Casualty Loss Reserve SeminarBoston, 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

)()1( dfdF

)1/()()()()1(2 BBBB dfdfdfdF

2)()1( dfdF

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