Ordered Random Vectors and Equality in Distribution

Abstract

In this paper we show that under appropriate moment conditions, two supermodular ordered random vectors with equal expected utilities (or distorted expectations) of the sums for an appropriate utility (or distortion) function, must necessarily be equal in distribution. The results in this paper can be considered as generalizations of the results of Cheung (2010), who presents necessary conditions for a random vector to be comonotonic, using the distribution of the sum.

Keywords: supermodular order, concordance order, expected utility, distorted expectation, comonotonicity