Optimal Saving under General Changes in Uncertainty: A Nonexpected Utility Maximizing Approach

Abstract

There has been an extensive discussion of optimal consumption-saving behavior of expected utility maximizing risk averse individuals [6; 7]. There are, however, two limitations of such works. First, the widely used time additive von Neumann Morgenstern (VNM) preferences may not be suitable for analyzing choice problems in a dynamic context. Since for this class of preferences the coefficient of relative risk aversion turns out to be the reciprocal of the elasticity of intertemporal substitution, these preferences fail to distinguish between the importance of intertemporal substitution and risk aversion in determining the optimal choice for the individual decision maker. Secondly, in analyzing the comparative static effect of an increase in risk, the increase in risk has been usually captured by the mean preserving spread of the distribution of the underlying random variable. But, since the mean of the distribution is stipulated to be unchanged, the mean preserving spread, undoubtedly, provides a restrictive characterization of an increase in risk. The limitation of the VNM preferences has motivated researchers to look for an alternative framework to analyze dynamic choices under uncertainty. It was Selden [8; 9] who developed a nonexpected utility maximizing approach by proposing the Ordinal Certainty Equivalent (OCE) preferences to distinguish between intertemporal substitution and risk aversion. Since then a number of other authors have further examined the implications of the nonexpected utility maximizing framework. Not surprisingly, in the literature of nonexpected utility maximizing analysis a considerable attention has been given to the individual saving decision under capital risk. In a clear departure from the expected utility maximizing analysis, under the nonexpected utility maximizing approach, optimal saving tends to be determined by the elasticity of intertemporal substitution as well as the risk aversion parameter. However, even in the nonexpected utility maximizing framework, the increase in capital risk has usually been characterized in terms of a mean preserving spread of the random rate of return. It has been shown by Selden [9] and Weil [10] that the effect of an increase in capital risk on the level of saving depends only on the elasticity of intertemporal substitution and not on the risk