November 16, 2005

1
Tail Factors Working Party Casualty Actuarial
Society2005 Annual MeetingRenaissance
Harborplace HotelBaltimore, Maryland presented
byF. Douglas Ryan, FCAS, MAAA

• November 16, 2005

November 3, 2005
2
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
Page 2
3
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.

Page 3
4
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.

Page 4
5
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.

Page 5
6
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

Page 6
7
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)

Page 7
8
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

Page 8
9
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
• Determination of Outstanding Liabilities for
  ULAE, Wendy Johnson, ACAS, MAAA
• Annuity Densities with Application to Tail
  Development, Dan Corro
• A Flexible Framework For Stochastic Claims
  Reserving, Peter D. England and Richard J.
  Verrall
• Unbiased Loss Development Factors, 1993
  Proceedings pp. 154-222, Daniel M. Murphy
• Generalized Bondy Development, Alfred O. Weller
• Estimation of Long-Tailed Unpaid Losses From
  Paid Loss Development Using Trended Generalized
  Bondy Development, Bradford S. Gile
• Extrapolating, Smoothing, and Interpolating
  Development Factors, Sherman
• Casualty Loss Reserving Seminar All teaching
  papers
• Using the Whole Triangle to Estimate Loss
  Reserves, Frank Pierson
• Performance Testing Aggregate and Structural
  Reserving Methods A Simulation Approach,
  Rollins
• Projecting Development of Losses During an
  Accident Year, Gogol

Page 9
10
Tail Factors Working Party

• Attempting to Test Various Methods
• Using Data Obtained From
• Three Insurance Companies
• Rating Bureau Data
• Schedule P Data
• RAA Data
• Difficulties
• Various data sets with differences in details
  available leading to inability to complete
  analysis
• Certain methods only applicable to specific types
  of data
• No clear testing method applicable to all methods
• Suggestion Future testing needed on simulated
  data

Page 10
11
Tail Factors Working Party

• Final Paper Expected to Identify 6 Major
  Groupings of Methods
• Bondy - Type
• Algebraic - Relationship Between Paid and
  Incurred Data
• Benchmark Data
• Stochastic and Curve Fitting
• Count Based
• Open Claim Characteristics

Page 11
12
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.

Page 12