Transcript Document 7257027

Report of the Tail Factor Working Party
Steven C. Herman, FCAS, MAAA
San Diego, California
September 10-11, 2007
Tail Factor Working Party
Co-Chairs
Steven C. Herman
Mark R. Shapland
Members
Mohammed Q. Ashab
Richard Kollmar
Joseph A. Boor
Rasa V. McKean
Anthony R. Bustillo
Michael R. Murray
David A. Clark
Bernard A. Pelletier
Robert J. Foskey
Anthony J. Pipia
Sejal Haria
F. Douglas Ryan
Bertram A. Horowitz
Scott G. Sobel
Gloria A. Huberman
Tail Factor Working Party
Disclaimer:
While this paper is the product of a CAS working
party, its findings do not represent the official view of
the Casualty Actuarial Society. Moreover, while we
believe the approaches we describe are very good
examples of how to address the issue of estimating
development of loss and loss adjustment expense
payments from a given evaluation to ultimate
disposition, we do not claim they are the only
acceptable ones, nor do they represent all possible
applications of the specific methods presented.
The Motivation
•
Tail factors used to estimate additional development
occurring
– after the eldest maturity in a given loss development triangle, or
– after the eldest credible link ratio.
• Over the years, many valuable contributions have been
made to the CAS literature describing methods for
calculating tail factors.
• However no overall paper compiling these contributions
existed.
The Paper
• The CAS Tail Factor Working Party
prepared this paper on the methods
currently used by actuaries in estimating
loss development tail factors.
• Standard terminology for discussing
aspects of link ratios and tail development
is communicated within the paper.
The Paper
• Included are
– Descriptions of advantages and disadvantages
of each method and
– Identification of what entities (companies,
rating bureaus, or consulting firms) typically
use each method.
Paper Description
• 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 Description
• Standard Notation:
– Consistency,
– Started with Notation from Reserve Variability
Working Party
– Added new notation where lacking
• Summarize Areas for Future Research
Section Description
• Bondy-Type Methods
• Algebraic Methods
• Benchmark Methods
• Open Claim Methods
• Curve Fitting Methods
• Lifespan Methods
• Miscellaneous Methods
Bondy-Type Methods Description
• Bondy Method
– Use last link ratio:
• Modified Bondy Method
2
– Double or square: F (d  1)  f (d )
• Generalized Bondy Method (Weller)
– For 0<B<1:
F (d  1)  f (d )
B
f (d )
B2
  f (d ) B /(1 B )
• Fully Generalized Bondy Method (Gile)
– Let Vary by Accident Year
Bondy-Type Methods Description
• 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 Description
• 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 Description
• 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 Description
• 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 Description
• 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 Description
• Maximum Possible Loss
• Judgment of Open Claim Costs / Audit
Open Claim Methods Description
• 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 Severe or IBNR/Reopened Claims
Curve Fitting Methods Description
• 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 Description
• 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 Description
• 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 Description
• 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 Description
• Restating Historical Experience via a
Claims Audit
– Adjust for Changes
Miscellaneous Methods Description
• 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