Tail Factor Methods in Actuarial Estimation

1. Tail Factors Working PartyCasualty 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 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 Productfor 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 Purposeis 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/literaturefor 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