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Quarterly Review
The Drama of Actuarial History
Society of Actuaries 50th Anniversary Monograph edited by James C. Hickman
(Society of Actuaries, 1999, $45.00)Reviewed by Sholom Feldblum
In 1999, the Society of Actuaries celebrated its 50th anniversary. As befits a learned body, the SOA issued a commemorative monograph with seven seminal articles in actuarial science from the Transactions. The large paperbound volume, with clear type on soft-toned pages, beckons the reader to step into the drama of actuarial history.
SOA actuaries, all of whom received the anniversary volume from the society, will gain from rereading the papers that set the direction of their science. Casualty actuaries who take the time to read it will gain double.
We seek to expand the borders of actuarial science, turning to financial economics and investment theory. SOA actuaries see a similar future for their own society. Yet a wall has risen between the two societies. We share mathematical foundations, we perform parallel functions, yet our sciences have diverged. We underwrite and price policies; we pay claims and set reserves. They also underwrite and price policies; they also pay claims and set reserves. We have no idea how they price their policies or set their reserves; they have no idea how we price our policies or set our reserves.
The Anderson Method
The seven papers in this volume signal turning points in actuarial thought. For instance, we measure insurance profitability by comparing the losses and expenses incurred in a given calendar year or policy year with the premiums earned in that year. In 1959, James Anderson realized the error in this perspective. The relevant business decision is the underwriting decision. The underwriting decision is judged by the present value of all future losses and expenses on the policy and on its renewals compared with the present value of present and future premiums on that policy and its renewals. Anderson's paper entitled "Gross Premium Calculation and Profit Measurement for Nonparticipating Insurance" develops the required exhibits to measure the value of insurance underwriting.
Anderson's paper changed the course of life insurance pricing. The SOA recognized his genius, and the paper was awarded the society's Triennial Prize for 1959-1961. (I first read this paper 12 years ago, and I replicated Anderson's method for personal auto premiums in a paper that received the 1996 CAS Dorweiler Prize.)
Casualty actuaries should not be content with reading a personal auto version of Anderson's method; they should read the original paper. Until now one had an excuse for sloth—it is hard to find a copy of the 1959 Transactions. Now that this paper has been republished in the SOA Anniversary volume, it behooves casualty pricing actuaries to master the Anderson pricing method.
Cumulative Antiselection Theory
Many years ago, casualty companies wrote most medical insurance in this country. Now SOA actuaries are the experts in health insurance pricing. Some casualty actuaries think that they can price individual medical insurance equally well. After all, do not workers compensation, general liability, and automobile insurance all pay for medical losses?
Medical insurance pricing is unique, because of a powerful informational asymmetry and the resulting "antiselective" lapsation. Healthy insureds often let their policies expire as they age and premiums increase; unhealthy insureds do not fail to renew.
In 1982, William Blume developed his cumulative anti-selection theory to model the progress over time of a book of medical insurance business. He quantified the effects, and he showed pricing actuaries how to anticipate the results of mid-term rate increases that accelerate the antiselective lapsation. Blume's paper won the society's 1980-82 Triennial Prize.
For many years, the CAS has directed its Syllabus Committee to keep health insurance ratemaking on its exams, and year after year I would recommend to the committee to put Blume's seminal paper on the syllabus. This is a paper we should all read—both Fellows and students—and it is now accessible to us in the anniversary monograph.
Interest Rate Generators
In the past few years, both actuarial societies have turned to financial modeling and investment analysis, with seminars and new papers for actuaries and with restructured exams for students. An essential element of many models is the interest rate process; a good model should have a realistic interest rate generator.
Actuaries are well-versed in modeling. We model loss frequencies with Poisson distributions and loss severities with Pareto distributions; why should interest rates be any different? Well, interest rates are much harder. When one fits a curve to loss frequencies, the result is never "wrong." But an interest rate generator implicitly determines the present values of the universe of risk-free bonds. If the generator produces values that differ from market values, the generator is in some sense "wrong," since it is not arbitrage free.
Almost no simple generators are arbitrage free, and we do not know how best to structure our models. Many actuaries are intimidated by the complexity of the more sophisticated models. In 1992, James Tilley published his "Actuarial Layman's Guide to Building Stochastic Interest Rate Generators." ("Layman" may be misleading; Tilley pointedly says "actuarial layman," who is an expert among laymen.) The paper won the society's 1992-93 Annual Prize, and it is an excellent introduction for the serious actuary.
There are four other papers in the volume: Jenkins and Lew on annuitant mortality; Trowbridge on pension funding; Fraser, Miller, and Sternhell on variable life; and Stiefel on guaranteed investment contracts. The variety of topics, and the high quality of these papers, make the SOA 50th Anniversary Monograph a wonderful volume for casualty actuaries.