Multivariate stochastic dominance for multivariate normal distribution

summary:Stochastic dominance is widely used in comparing two risks represented by random variables or random vectors. There are general approaches, based on knowledge of distributions, which are dedicated to identify stochastic dominance. These methods can be often simplified for specific distribution. This is the case of univariate normal distribution, for which the stochastic dominance rules have a very simple form. It is however not straightforward if these rules are also valid for multivariate normal distribution. We propose the stochastic dominance rules for multivariate normal distribution and provide a rigorous proof. In a computational experiment we employ these rules to test its efficiency comparing to other methods of stochastic dominance detection