James C. Hickman

Notes on the dynamics of pension funding

Abstract The authors follow up some previous work on the dynamics of pension funding by three notes. The first of these concerns contribution rates consisting of the normal cost plus a generalized amortization method for unfunded supplemental present value (actuarial accrued liability). The second note examines aggregate cost funding for active members when there exist consistent difference between the assumed and the actual rates of interest and of growth. The third note explores the operation of a variable annuity system in the context of our general model for pension funding dynamics.

“A Re-examination of the Joint Mortality Function,” Heekyung Youn, Arkady Shemyakin, and Edwin Herman, January 2002

BRUNO, M. G., E. CAMERINI, AND A. TOMASSETTI. 2000. “Financial and Demographic Risks of a Portfolio of Life Insurance Policies with Stochastic Interest Rates: Evaluation Methods and Applications.” North American Actuarial Journal 4(4): 44–55. CACCIAFESTA, F. 2001. “Discussions of Papers Already Published.” North American Acturial Journal 5(4): 112–14. PARKER, G. 1997. “Stochastic Analysis of the Interaction between Investment and Insurance Risks.” North American Actuarial Journal 1(2): 55–84.

Pensions and Sex

The issue of the use of sex as a classification variable in defining pension benefits is being discussed in several forums. As this is written, the issue is before the Supreme Court of the United States in the form of the case Arizona Governing Committee for Tax Deferred Annuities vs. Norris. In this judicial forum the issue is described in legal terms. That is, does the fact that the woman, Norris, received a smaller monthly life income from her accumulated deferred compensation than she would have received if she had been a man constitute a violation of Title VII of the Civil Rights Act of 1964? At the same time, within a legislative forum, the Congress is considering the broader public policy issue of the use of sex as a classification factor in insurance of all types. The Non-discrimination in Insurance Act (S. 372 and H.R. 100) is designed to achieve this broad goal. The issue is also being discussed in the academic forum, as certified by the accompanying paper by Christiansen [ 1]. In this essay several aspects of the issue will be explored. First, however, a foundation must be built.

INVESTMENT IMPLICATIONS OF THE ACTUARIAL DESIGN OF LIFE INSURANCE PRODUCTS

The traditional design of life insurance products marketed in the United States has included level premiums graded by initial age, fixed dollar benefits, and relatively high withdrawal benefits. This design has certain implications on life insurance investments. Because of the long term and fixed dollar nature of life insurance liabilities, investments with similar characteristics are indicated. In recent years, marked with both price inflation and real economic growth, the purchasers of the products and services of life insurance companies have seemed to place less value on investment guarantees. A new family of products and services is being developed that will cause a shift in the investment objectives of life insurance companies.

INSURANCE PREMIUMS AND DECISION ANALYSIS

Recent criticisms of the principles and procedures by which insurance premiums have been determined are reviewed. Examples are developed which illustrate the application of the methods of decision analysis to the determination of insurance premiums. Problems such as the measurement of consumer demand for insurance and the quantification of management objectives, which tend to remain in the background in conventional approaches to insurance premiums, must be squarely faced in applying decision analysis. Examples of how Bayesian decision methods may be used to modify initial insurance prices as experience unfolds and to arrive at rational decisions concerning ancillary benefits and options in insurance policies, are presented. The definition of the actuarial function that appears in the organizational chart of most insurance corporations, the dictionary definition of actuarial science, and the description in a university catalogue of a course in actuarial science will usually agree that actuarial science is concerned with the determination of the price of insurance protection. Traditionally one of the primary thrusts in actuarial education has been directed toward teaching students the mathematical techniques through which the present expected value of future insurance benefits, which may be uncertain in amount and occur at uncertain times, and the present ex

Connections Between Graduation and Forecasting

The motivation for the development of graduation methods is usually based on one of two foundations: 1. Mathematical programming. An objective function is specified and the set of graduated values is found so that an optimal value of the objective function is attained. 2. Statistical analysis. A statistical model is specified and the set of graduated values that attain a goal stated in statistical terms such as minimum variance or a posterior mean is found.

A comparison of several life table estimation methods

Abstract Occurrence/exposure, integrated force, product limit, and classical actuarial frequency estimators are compared via simulation. Impacts of different sampling designs, different periods of observation, different sample sizes, and different withdrawal patterns are exhibited.

E. J. Moorhead (1910 – 2004)

Jack Moorhead did it all. He was born in Winnipeg, Manitoba, on January 23, 1910 and died in Hanover, New Hampshire, on February 21, 2004. During the intervening ninety-four years, he created a remarkable set of family and professional achievements and served the public in an unswerving fashion. In his Presidential Address to the Society of Actuaries, Jack (1970) even set goals for obituary writers. “If the deceased is known to be a person who contributed in some special way to the history of this organization, we ought to see that this is noted for posterity, even if this has to be done by supplemental reminiscences of contemporaries.” As expected, this is good advice but difficult to follow in Jack’s case. He influenced the development of so many actuarial ideas and played a pivotal role in so many organizational issues that it is hard to know where to begin. Adapting the U. S. Social Security system to the new demographic realities continues as a subject of political discussion and remains near the top of the actuarial agenda. Jack was there at the beginning. In a paper with C. L. Trowbridge (1977), Jack described his participation in developing social security reform proposals. The 1977 paper was particularly interesting because it discussed the merits and demerits of wage and price indexing of wage histories in computing Average Indexed Monthly Earnings (AIME). The AIME is a key input in determination of the basic benefit, the Primary Insurance Amount (PIA) in Social Security. Trowbridge favored wage indexing and Moorhead favored price indexing. The issue was resolved in favor of wage indexing by the 1977 Social Security Amendments, but the issue did not die. Price indexed wage histories are back on the table as a rational method of slowing benefit growth. The efficient operation of a market economy

“Principal Applications of Bayesian Methods in Actuarial Science: A Perspective”, Udi E. Makov, October 2001

nadian Journal of Statistics 19(1): 57–65. ———. 1993. “Robust Bayesian Diagnostic,” Journal of Statistical Planning and Inference 35: 171–88. SIVAGANESAN, S., AND J. O. BERGER. 1989. “Ranges of Posterior Measures for Priors with Unimodal Contaminations,” The Annals of Statistics 17(2): 868–89. VENTER, G. 1991. “Effects of Variations from Gamma-Poisson Assumptions,” Proceedings of the Casualty Actuarial Society 78: 41–56. YING-HSING, L., AND Y. MING-CHUNG. 1997. “Posterior Robustness in Simultaneous Estimation Problem with Exchangeable Contaminated Priors,” Journal of Statistical Planning and Inference 65: 129–43. YOUNG, V. R. 2000. “Credibility Using Semiparametric Models and a Loss Function with a Constancy Penalty” Insurance: Mathematics and Economics 26(1): 151–6.