Transcript Tail Factors Working Party Casualty Actuarial Society 2005 Annual Meeting Renaissance Harborplace Hotel Baltimore, Maryland presented by F.

Tail Factors Working Party
Casualty Actuarial Society
2005 Annual Meeting
Renaissance Harborplace Hotel
Baltimore, Maryland
presented by
F. Douglas Ryan, FCAS, MAAA
November 16, 2005
November 3, 2005
Tail Factors 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
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Tail Factors 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.
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Tail Factors Working Party
The Motivation
Tail factors are used by actuaries to estimate the additional development
that will occur 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 which
describes various methods for calculating tail factors. The CAS Tail
Factors Working Party prepared this paper on the methods currently
used by actuaries to estimate loss development ‘tail’ or ‘completion’
factors. Standard terminology for discussing aspects of link ratios and tail
development is communicated within the paper. Descriptions of the
advantages and disadvantages of each method are included as well
general indications of what entities (companies, rating bureaus, or
consulting firms) typically use each method.
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Tail Factors Working Party
•
Last year we identified that:
– The Product for this Working Party will be a paper which will
• Survey existing literature
• Identify additional methods in use
• If needed, identify further areas that may need to be researched.
• Product may provide examples of results using identified methods
on industry data.
– The Purpose is both to educate students and to help practitioners. It
may become part of the syllabus and/or be included in a reserving
textbook.
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Tail Factors Working Party
• In the last 11 months, we have:
– Had 30+ Conference Calls - Full Working Party
– Had Numerous Conference Calls by 11 Task Groups
– Identified about 25 methods
– Attempted to test various methods
– Created a preliminary draft of 114 pages for submission to
reviewers
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Tail Factors Working Party
• Example of Task Groups (some were consolidated):
– Survey Existing CAS literature
– Survey literature contained in other disciplines’ publications
– Survey of methods used by insurance companies, reinsurers, rate
bureaus, consulting firms, regulators
– Identify and research feasibility in obtaining test data (industry
consolidated sources, statistical reporting agencies, bureaus,
companies, models)
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Tail Factors Working Party
• Example of Task Groups (some were consolidated):
– Develop a standard methodology and measurable statistics to
compare identified methods results on test data
– Apply methods to test data and prepare summary statistics
– Write up of identified methods and test results
– Consolidation of work of other task groups into a draft paper for
review
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Tail Factors Working Party
Results for One Major Task Group –Survey of CAS Literature
–
–
Task Group reviewed 35 articles/literature for tail factor methodologies
Identified following 11 as useful for our research of loss development tail factor methodologies
1. “Determination of Outstanding Liabilities for ULAE,” Wendy Johnson, ACAS, MAAA
2. “Annuity Densities with Application to Tail Development,” Dan Corro
3. “A Flexible Framework For Stochastic Claims Reserving,” Peter D. England and Richard
J. Verrall
4. “Unbiased Loss Development Factors”, 1993 Proceedings pp. 154-222, Daniel M. Murphy
5. “Generalized Bondy Development,” Alfred O. Weller
6. “Estimation of Long-Tailed Unpaid Losses From Paid Loss Development Using Trended
Generalized Bondy Development,” Bradford S. Gile
7. “Extrapolating, Smoothing, and Interpolating Development Factors,” Sherman
8. Casualty Loss Reserving Seminar – All teaching papers
9. “Using the Whole Triangle to Estimate Loss Reserves,” Frank Pierson
10. “Performance Testing Aggregate and Structural Reserving Methods: A Simulation
Approach,” Rollins
11. “Projecting Development of Losses During an Accident Year,” Gogol
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Tail Factors Working Party
•
Attempting to Test Various Methods
–
Using Data Obtained From:
1. Three Insurance Companies
2. Rating Bureau Data
3. Schedule P Data
4. RAA Data
–
Difficulties
1. Various data sets with differences in details available leading to
inability to complete analysis
2. Certain methods only applicable to specific types of data
3. No clear testing method applicable to all methods
4. Suggestion – Future testing needed on simulated data
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Tail Factors Working Party
•
Final Paper Expected to Identify 6 Major Groupings of Methods:
1.
2.
3.
4.
5.
6.
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Bondy - Type
Algebraic - Relationship Between Paid and Incurred Data
Benchmark Data
Stochastic and Curve Fitting
Count Based
Open Claim Characteristics
Tail Factors Working Party
• In a future Forum, we expect that:
– The paper for this Working Party will be released which
• Surveys existing literature
• Identifies additional methods in use
• Identify further areas that may need to be researched.
• Provides examples of results using identified methods
– We expect that it will meet the purpose of both educating students
and helping practitioners and that it will become part of the
syllabus and/or be included in a reserving textbook.
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