Additional Aspects of Rational Insurance Purchasing

Abstract

The purchase of insurance provides an individual with the ability to shift risk associated with either timeless or temporal uncertain prospects (see Dreze and Modigliani 1972). Previous insurance decision analysis can be further divided into cases in which the insurance contract is exogenously specified (see Mossin 1968; Smith 1968) and cases in which the optimal form of contract is to be determined (see Raviv 1979; Brennan and Solanki 1981). This note is concerned with extending some of the results for timeless uncertain prospects with the insurance contract exogenously specified. Many of the properties associated with the purchase of insurance for timeless uncertain prospects are analyzed by Mossin (1968) for different forms of contracts (see also Gould 1969). Utilizing the Arrow-Pratt measure of absolute risk aversion, the effect of wealth upon the optimal amount of insurance is determined for the different forms of contracts. Recent work by Ross (1981) demonstrates that in situations where individuals face more than one (timeless) uncertain prospect and they can purchase insurance only for a subset of these prospects, then a more risk-averse individual in the Arrow-Pratt This paper examines the use of the ArrowPratt and Ross measures of risk aversion. It is shown that in situations where the individual faces more than one uncertain prospect and can purchase insurance only for a subset of these prospects. then in many cases the Arrow-Pratt and Ross measures of risk aversion are not sufficient to describe the behavior of the individual in purchasing insurance.