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

See all articles by Ka Chun Cheung

Ka Chun Cheung

The University of Hong Kong

Jan Dhaene

Katholieke Universiteit Leuven

Alexander Kukush

Catholic University of Leuven (KUL)

Daniël Linders

University of Illinois

Multiple version iconThere are 2 versions of this paper

Date Written: January 11, 2013

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 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

Suggested Citation

Cheung, Ka Chun and Dhaene, Jan and Kukush, Alexander and Linders, Daniël, Ordered Random Vectors and Equality in Distribution (January 11, 2013). KU Leuven - Faculty of Economics and Business Working Paper No. AFI_1377. Available at SSRN: https://ssrn.com/abstract=2261656 or http://dx.doi.org/10.2139/ssrn.2261656

Ka Chun Cheung

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, Pokfulam HK
China

Jan Dhaene (Contact Author)

Katholieke Universiteit Leuven ( email )

Naamsestraat 69
Leuven, 3000
Belgium

Alexander Kukush

Catholic University of Leuven (KUL) ( email )

Leuven, B-3000
Belgium

Daniël Linders

University of Illinois ( email )

306 Altgeld Hall,
1409 West Green Street
Champaign, IL 61822
United States

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