paper overview
DESCRIPTION
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. Organized by “Type” of Method Sections Describe: Mechanics of each method, Examples for most methods, Results of our Testing, and - PowerPoint PPT PresentationTRANSCRIPT
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