Best Estimates for Reserves

Insureware is pleased to announce that “Best Estimates for Reserves”, by Dr. Glen Barnett and Professor Ben Zehnwirth, is included in the list of readings for the 2005 CAS Syllabus of Examinations. “Best Estimates for Reserves” is published in the Proceedings of the CAS, Volume LXXXVII, 2000, pp. 245-303 and is available at:

A list of errata is available pdf here (10 KB) . A spreadsheet that illustrates the calculations for the regression equivalent of chain ladder link ratios can be found Archive here (98 KB) .

Answers to FAQs will be added below:

 Abstract of “Best Estimates for Reserves”

Link-ratio techniques can be regarded as weighted regressions. We extend these regression models to handle different exposure bases and modeling of trends in the incremental data, and develop a variety of diagnostic tools for testing the assumptions of these models.

This ‘extended link-ratio family’ (ELRF) of regression models is used to test the assumptions made by standard link-ratio techniques and compare their predictive power with modeling trends in the incremental data. Most loss arrays don't satisfy the assumptions of standard link-ratio techniques. The ELRF modeling structure creates a bridge to a statistical modeling framework where the assumptions are more consistent with actual data. There is a paradigm shift from standard link-ratio techniques to the statistical modeling framework - the ELRF models form a bridge from the ‘old’ paradigm to the ‘new’.

There are three critical stages involved in arriving at a reserve figure: extracting information from the data in terms of trends and stability, and distributions about these trends; formulating assumptions about the future leading to forecasting of distributions of paid losses; and correlation between lines and security level sought.

Other benefits of the new statistical paradigm are discussed, including segmentation, credibility and reserves or distributions for different layers.

 A review of the paper entitled: “Barnett and Zehnwirth Provide Road Map for Probabilistic Reserve Models”, by Frederick F. Cripe, Chairperson, CAS Research Policy and Management Committee, is available at

The following are a number of excerpts from Cripe’s review:

“Although the actuarial literature is replete with articles explaining the shortcomings of the traditional link ratio methods, most actuarial reserve analyses mainly rely on link ratio methods.”

“‘Best Estimates for Reserves’ Glen Barnett and Ben Zehnwirth provide an outstanding discussion of the relationship between traditional link ratio methods, broader regression models, and probabilistic reserve estimation models.”

“Barnett and Zehnwirth have written an excellent paper that provides a flexible and powerful set of methods for estimating reserves.”

Guide to the paper: "Best Estimates for Reserves"

An additional set of study notes (powerpoint slides) designed to aid the understanding of the paper: "Best Estimates for Reserves" is available Archive here (1.82 MB) . This guide was written to make the paper easier to read.

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