Transcript Tail Factors Working Party: Part 2. The Work Product

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
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Organized by “Type” of Method
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Sections Describe:
– Mechanics of each method,
– Examples for most methods,
– Results of our Testing, and
– Results of our Surveys
Paper Overview
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Standard Notation:
– Consistency,
– Started with Notation from Reserve
Variability Working Party
– Added new notation where lacking
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Summarize Areas for Future Research
Section Overview
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Bondy-Type Methods
Algebraic Methods
Benchmark Methods
Open Claim Methods
Curve Fitting Methods
Lifespan Methods
Miscellaneous Methods
Bondy-Type Methods
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Bondy Method
– Use last link ratio: F (d  1)  f (d )
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Modified Bondy Method
– Double or square: F (d  1)  f (d ) 2
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Generalized Bondy Method (Weller)
– For 0<B<1: F (d  1)  f (d ) f (d )   f (d ) B /(1 B)
B
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B2
Fully Generalized Bondy Method (Gile)
– Let Vary by Accident Year
Bondy-Type Methods
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Advantages
– Simple to Implement
– Pattern Described with One Factor
– Only Requires Cumulative Paid Data
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Disadvantages
– Not Always Useful for Incurred Data
– Will Fail with Increasing Development
– May Fail with “More Complicated” Patterns
Algebraic Methods
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Equalizing Paid & Incurred Loss
Estimates
– Use Cumulative Incurred / Cumulative Paid
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Boor’s Method
– Adjust Case Reserves
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Mueller’s Method
– Adjust Incremental Factors
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NCCI Method
Algebraic Methods
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Advantages
– Simple to Implement
– Only Requires Cumulative Data
– Statistically Unbiased
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Disadvantages
– May Not be Sophisticated Enough
– Subject to Case Reserve Distortions
– Some Methods Not Generally Well Known
Benchmark Methods
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Benchmark Development / Link Ratios
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Adjusted Benchmark Development /
Link Ratios
– Use Link Ratios to Adjust Tail Factor
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Benchmark Average Severity
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Benchmark Adjusted by Claims Audit
Benchmark Methods
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Advantages:
– Supplement when Little Data
– Adds Credibility
– Various Degrees of Sophistication
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Disadvantages:
– Need Similar Data
– Claim Handling Procedures
– Relative Case Reserve Strength
Open Claim Methods
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Maximum Possible Loss
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Judgment of Open Claim Costs / Audit
Open Claim Methods
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Advantages:
– Incorporates Particulars of Open Claims
– Uses Knowledge of Claim Staff
– Can Provide Bounds
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Disadvantages:
– Requires Access to Individual Claims
– Subject to Judgment/Availability of Auditors
– May Underestimate for Severe Cases
Curve Fitting Methods
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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
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Advantages:
– Straightforward & Intuitive
– Extrapolate Beyond End of Data
– Various Levels of Sophistication
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Disadvantages:
– May Underestimate Tail for Long-Tail Lines
– Sub-Optimal If Pattern Not Consistent
– Sometimes No Closed Form Solution
Lifespan Methods
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Static Mortality Method
– Frequency / Severity Using Mortality Rates
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Trended Mortality Method
– Greatest Impact on “Distant” Years
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Sherman-Diss Method
– Separate Impact of Inflation & Mortality
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Corro’s Method
– Modeling of “Pension” Claims
Lifespan Methods
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Advantages:
– Extrapolate “Very-Long” Tail
– Can Include “Increasing” Factors
– Detailed Assumptions/Some Non-Subjective
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Disadvantages:
– More Complex
– Need “Very Old” Data to Parameterize
– Need Specific Mortality Rates
Miscellaneous Methods
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Restating Historical Experience via a
Claims Audit
– Adjust for Changes
Miscellaneous Methods
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Advantages:
– Improves “Other” Methods
– Adjustments Readily Understood
– Add Claim Professional Judgment
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Disadvantages:
– Difficult to Reconstruct Old Claim Files
– Auditor Must Ignore Prior Development
– Auditor Must Evaluate at Multiple Points