Monte Carlo Evaluation of Life Insurance Strategy

Abstract

This paper describes an experiment in which the Monte Carlo method is applied to the problem of evaluating alternative life insurance strategies. A hypothetical family is modeled and family wealth is observed during a forty year life cycle under a variety of assumptions concerning life insurance and other financial decisions. The basic objective is exploration of methodological adequacy for evaluating life insurance strategy. The model is used to gather general insights as to preference for different strategies under stochastic dominance ordering rules. A methodology for estimating the cost of life insurance protection is also explored. The evaluation of life insurance strategy is an important part of the problem of consumer choice. Viewed in the framework of time-state preference,1 the insurance decision is a significant factor in determining uncertain wealth outcomes. This is clearly evident in the increasing attention devoted to such variables as uncertainty of lifetime and bequest motivation in models of consumer choice.2 But theoretical models are difficult to operationalize. In view of the variety of available life insurance programs, with complex and time-variant costs and benefits, realistic insurance models are mathematically intractable. Operational techniques for solving insurance models are also elusive. Stochastic dynamic programming, for example, is an attractive and logical framework for choice models. But algorithms are not available for extended time horizons and data deficiencies are severe. Cross-section panel data exist but individual time series of consumption, savings and wealth do not. In view of the mathematical and empirical problems involved, simulation is a promising alternative methodology. This paper discusses the construction, operation and testing of a Monte Carlo insurance model. It introduces Anthony J. Curley, Ph.D., C.P.A., is Associate Professor of Finance in The Pennsylvania State University. His earlier teaching was at St. Joseph's College and The Wharton School. This paper was submitted in June, 1973. This study was made possible by a research grant from the American Risk and Insurance Association. Additional support and computer resources were made available by the P.S.U. Center for Research of the College of Business Administration. The author is indebted to Richard Parli for research assistance, to R. Burr Porter for useful comments on an earlier draft, and to participants at the 1973 Risk Theory Seminar for their comments and encouragement. 'See Arrow [1], Debrew [5] and Hirshleifer [11]. 2Insurance has been considered in theoretical choice models by, among others, Fama [6], Hakansson [9], Meade [15], Merton [16], Samuelson [21] and Yaari [24, 25].