Computing sets of expected utility maximizing distributions for common utility functions

Abstract

The set of distribution functions that maximize expected utility for some utility function in a given class is the optimal set. This paper presents an algorithm for determining the optimal set of distributions for an important class of preferences and general finite sets of alternatives. The class of preferences considered, which includes the commonly used log, exponential and power functions, is the set of utility functions with complete monotone marginal utility (all derivatives alternate in sign). The algorithm is based on the necessary and sufficient conditions for infinite degree convex stochastic dominance, and is implemented using the solutions to a parametric family of linear programming problems. The algorithm is intended to be applied to sample data, and nonparametric statistical inference procedures are provided.