Multivariate decision-making

Consider a set of multivariate risky options. A partial ordering of these options is quite difficult, and even for the two-dimensional case a knowledge of the cross derivatives of the decision-maker's utility function is required. In this paper we establish first-degree multivariate stochastic dominance by applying the concepts of the indirect utility function and the indirect probability distribution. Thus, we reduce the complex multivariate risky option into a univariate risky option where the random variable is the derived indirect income. The second-degree stochastic dominance rule is also derived under certain restrictions on the utility function.