Abstract
The last ten years have seen extensive research effort devoted to problems of multiperiod resource allocation in an uncertain setting. Two primary areas of study have been the theory of optimal growth (e.g., Brock and Mirman, Mirrlees and Mirman and Zilcha) and the multiperiod consumption/savings (portfolio) problem (e.g., Levhari and Srinivasan, Han, Hakansson, Samuelson and Merton). In both cases, especially the latter, it has been standard to assume first that the consumer possesses a complete preordering over joint distributions for consumption flows which is representable by a continuous multi attribute expected utility function and second that the NM (von Neumann-Morgenstern) index is additively separable and stationary. To obtain concrete answers to specific questions such as the effect of increased capital risk on savings, still another assumption is generally added: the consumer’s conditional risk preferences (for each time period) exhibit constant relative risk aversion. The purpose of this paper is two-fold. First of all, we present a preference-utility model which is more general than the additively separable multiperiod expected utility paradigm in that it allows one significantly greater freedom in prescribing risk preferences and time preferences. Secondly, we utilize this freedom in an application of the resulting theory to a simple multiperiod consumption/savings problem.