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Quarterly Review
The Essence of Loss Reserving
Loss Reserving: An Actuarial Perspective, by Greg Taylor
(Kluwer Academic Publishers, 2000, $139.95)
Reviewed by Kevin M. Madigan
The following article appeared in the September 2002 issue of The Journal of Risk and Insurance.
What does one mean by the phrase Loss Reserving? An accountant may feel that the phrase refers to the complicated accounting rules and regulations for recording liabilities in statutory annual statements. A financial officer may feel that the phrase refers to the process of examining the company's finances and arriving at the liabilities that will be recorded at the close of the next quarter. To a practicing actuary, Loss Reserving is the practice of estimating the future payments on a defined collection of claims, some of which may be unreported. This is the focus of Greg Taylor's book Loss Reserving: An Actuarial Perspective. It should be pointed out that Taylor's focus is on direct property and casualty insurance loss reserving; the text does not discuss loss reserving of assumed reinsurance or of life and health insurance losses.
It is an unfortunate fact that for many practicing actuaries the major challenges presented by a loss reserve analysis are related to data gathering and validation. One can become so concerned with the gathering, validating, "thinness," or credibility of the data, with how to properly organize and utilize it (e.g., "apples and oranges"), that the majority of one's time and resources are focused on these issues. In these situations, it is not unusual for the actuary to spend inordinate amounts of time and energy getting the data into proper shape, and then performing a rather anemic analysis using unadjusted paid and incurred loss triangles. This is partially a resource issue: it costs time and money to perform a rigorous analysis of liabilities. Another part of the problem is the lack of a widely recognized reference work on the topic of loss reserving. Taylor's book is a good candidate for filling this role. Throughout the text, the focus is on solving real problems presented by real data. There are numerous examples, and numerous questions are posed and answered. This text gives a good feel for the kinds of questions an actuary should ask when performing a reserve analysis, and for the thought processes involved in trying to answer them.
The structure of the book is sound, the text flows smoothly, and the author makes use of a single real-life data set to illustrate the techniques being discussed. The book is divided into two parts: Deterministic Models and Stochastic Models. In the first part, Taylor works from the ground up, beginning with a very brief description of the claims payment process. From the beginning, particular attention is paid to changes in underlying claims costs (i.e., inflation), and very early in the discussion of claim counts the chain ladder method is derived. The author actually presents three derivations of the chain ladder method and points out that, for all of its recognized flaws, this method occupies a key role in actuarial practice. Chapters 3, 4, and 5 round out the discussion of deterministic models, ending with the Bornhuetter-Ferguson and Cape Cod methods. The attention paid to the deterministic models and the techniques available for dealing with troubling data issues and/or inflation make this book a good primer on loss reserving, and a very useful reference for practicing actuaries. It should be particularly helpful to those tackling difficult reserve analyses.
Part II begins with the prerequisites [Generalized Linear Models (GLMs), filtering, bootstrapping] for stochastic reserving methods. The second part is almost modular in structure. After one has mastered the statistical prerequisites in Chapter 6, one can approach most of the other chapters independently. Chapters 7 through 11 cover the topics of stochastic chain ladder methods, stochastic models with a GLM basis, credibility models, Kalman filtering, and bootstrap methods. Chapter 12 wraps everything up with a discussion of how one uses the results of all of the previously discussed models to arrive at the selected liabilities. One of the appealing features of the book is that questions raised in Part I are used to motivate some of the development of Part II.
Despite all of the positive things mentioned above, I have mixed emotions about this text. It would be wonderful to have a book on this topic that is suitable for all reasonably foreseeable uses. (This is probably an unrealistic fantasy.) Alas, that is not what we have here. Taylor has written a fine text for graduate study and a fine reference for practicing actuaries and academic researchers. As a textbook, Loss Reserving is probably only appropriate for students with strong technical backgrounds, already accustomed to rigor and mathematical notation. That is not a bad thing, as the topic demands rigor —millions of dollars are in the balance —and a rigorous treatment of the subject should be a welcome component of graduate study in the financial economics of insurance. Unfortunately, some of the notation can get confusing. One could use sections of this text to structure a course for less sophisticated students if the proper care is taken in selecting those sections. Taylor's text is not a good candidate for self study by students who are not comfortable with modern mathematical rigor and notation; such students require a good instructor to navigate through the derivations and some of the subtler arguments. As a reference work for practicing actuaries and researchers in the field, Loss Reserving is quite good, though perhaps too rigorous and rich in notation for some tastes.
In summary, Greg Taylor has done a remarkable job of balancing the theoretical with the practical, and has produced a text that is an essential tool for researchers, for actuaries with loss reserving practices, and for students who are serious about the study of actuarial methodologies and the financial economics of insurance.
Copyright 2002 by the American Risk and Insurance Association, Malvern, Pennsylvania. Reprinted with permission.