Author:

Keywords:

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

Abstract:

In this paper we show that under appropriate moment conditions, the supermodular ordered random vectors X = (X1;X2; : : : ;Xn) and Y = (Y1; Y2; : : : ; Yn) with equal expected utilities (or distorted expectations) of the sums X1 +X2 +: : :+Xn and Y1 +Y2 +: : :+Yn for an appropriate utility (or distortion) function, must necessarily be equal in distribution, that is X d=Y . The results in this paper can be considered as generalizations of the results of Cheung (2010), who presents necessary conditions related to the distribution of X1 + X2 + : : : + Xn for the random vector X = (X1;X2; : : : ;Xn) to be comonotonic.