Ordered Random Vectors and Equality in Distribution
KU Leuven - Faculty of Economics and Business Working Paper No. AFI_1377
25 Pages Posted: 18 May 2013
Date Written: January 11, 2013
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 Xd=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.
Keywords: supermodular order, concordance order, expected utility, distorted expectation, comonotonicity
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