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Two Recent Proposals for Improving Reserve Ranges

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This webinar will present two papers from the CAS Reserve Call Paper program.
Both deal with ways to include correlation in estimating reserve ranges.

“Making Reserve Ranges More Realistic” by Clark, Ding and Zhou shows how correlation can be included in bootstrapping via a copula.

Backtesting suggests that bootstrapping approaches lead to reserve ranges that may be too narrow. To improve the current methods, we relax England and Verrall’s assumption that each cell in the incremental development triangle is independent by introducing a correlation structure in the resampling of the bootstrap. Backtesting with
Schedule P data suggests that this approach yields reserve ranges that are more reasonable.

Learning Objectives:

  1. Understand the current Bootstrapping methods and the results produced by these methods, including back-testing of the results.
  2. Describe a new variation to the current method that involves relaxation of the independence amongst resampling data.
  3. Learn the application of the new technique

“Quantifying Reserve Risk Based on Volatility in Triangles of Estimated Ultimate Losses” by Feng and Robbin examines correlations in age-to-age factors, and makes use of past estimates of ultimate loss.

This presentation explores the idea of quantifying reserve risk by looking at triangles of age-to-age factors of estimated ultimate losses. Such triangles implicitly reflect not only volatility of the paid and reported development factors used in deriving the estimates of ultimate, but also the accuracy of the process used in deriving the estimates of ultimate from the data. The general idea is to derive a formula for reserve variance based on the variance covariance matrix of the logs of the LDF. The presentation shows how the authors implemented their version of this approach. Their version fixes a major technical problem that can give rise to theoretically impossible correlation values. The authors show this problem stems from the triangle structure of the data. The presentation outlines the authors' formulas for one-year and ultimate reserve variance and compares these to formulas in the literature.

Learning Objectives:
  1. Introduce and explore the concept of measuring variability using ultimate loss
  2. Understand why other methods can lead to theoretically impossible variance-covariance values.
  3. Explain the various Feng-Robbin options for fixing the triangle structure problem.

Registration Information and Fees


Registration Fees (in U.S. Dollars) Received on/by
November 14, 2023
Received after
November 14, 2023
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  • David Clark

    David R Clark is a Fellow of the Casualty Actuarial Society (FCAS) and a member of the American Academy of Actuaries (MAAA). He works for Munich Reinsurance as part of the Actuarial Research and Modeling team in Princeton. Dave began his career in the insurance field at CIGNA Property & Casualty (now ACE USA Chubb) in Philadelphia in 1985 and joined Munich Reinsurance in 2000. He is known within the actuarial community for his study note on “Basics of Reinsurance Pricing” on the CAS examination syllabus. He was the recipient of the CAS’s Non-Technical Reserving Call Paper Prize in 2015 for his paper on “Accident Year and Development Year Interactions” co-written with Diana Rangelova.

  • Hang Ding

    Data Scientist at Hartford Steam Boiler. Joined Munich Re Group at 2020 as a senior actuarial analyst in corporate reserving department. Transferred to HSB ay May 2023.

  • Yu Shi "Andy" Feng

    Andy Feng is a capital modeling actuary working at TransRe. He has previously held risk and reserving roles in Starr Companies and PwC. Andy holds a Bachelor Degree in Mathematics from University of Waterloo, Canada. Andy is extensively involved in CAS volunteer activities, including those in the exam committee, the committee on risk, and the organizing committee for the ERM symposium and the Reinsurance Seminar.

  • Ira Robbin

    Dr. Ira L. Robbin, ACAS, is now semi-retired and living in Florida. He was most recently an Assistant Professor teaching Math and Statistics at Southern Connecticut State University in New Haven, Connecticut. Prior to that, he had a long actuarial career working in pricing, reserving, and capital modeling positions for several large insurers and reinsurers including TransRe, AIG, Endurance, ACE, and CIGNA. He has written papers and made numerous presentations on a range of conceptual and technical topics including catastrophe pricing, capital modeling, profitability, reserving, and credibility. He has an undergraduate degree in Math from Michigan State and a PhD in Math from Rutgers.

November 28, 2023
Tue 12:00 PM EST

Duration 1H 30M

This live web event has ended.

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