Multivariate Stochastic Dominance for Risk Averters and Risk Seekers

Abstract

This paper extends some well-known univariate stochastic dominance results to multivariate stochastic dominances for risk averters and risk seekers, respectively, when the attributes are assumed to be independent and the utility is assumed to be additively separable. Under these assumptions, we develop some properties of multivariate stochastic dominances for risk averters and risk seekers, respectively. For example, we prove that multivariate stochastic dominances are equivalent to the expected-utility maximization for risk averters and risk seekers, respectively. We show that the hierarchical relationship exists for multivariate stochastic dominances. We develop some properties for non-negative combinations and convex combinations of random variables of multivariate stochastic dominance. Finally, we establish some multivariate stochastic dominance relationships when attributes are dependent and discuss the importance and usefulness of the results developed in this paper.