Title

Multivariate stochastic dominance for risk averters and risk seekers

Document Type

Journal article

Source Publication

RAIRO-Operation Research

Publication Date

7-2016

Volume

50

Issue

3

First Page

575

Last Page

586

Publisher

EDP Sciences

Keywords

Multivariate stochastic dominance, risk averters, risk seekers, ascending stochastic dominance, descending stochastic dominance, utility function

Abstract

This paper first extends some well-known univariate stochastic dominance results to multivariate stochastic dominances (MSD) for both risk averters and risk seekers, respectively, to n order for any n ≥ 1 when the attributes are assumed to be independent and the utility is assumed to be additively and separable. Under these assumptions, we develop some properties for MSD for both risk averters and risk seekers. For example, we prove that MSD are equivalent to the expected-utility maximization for both risk averters and risk seekers, respectively. We show that the hierarchical relationship exists for MSD. We establish some dual relationships between the MSD for risk averters and risk seekers. We develop some properties for non-negative combinations and convex combinations random variables of MSD and develop the theory of MSD for the preferences of both risk averters and risk seekers on diversification. At last, we discuss some MSD relationships when attributes are dependent and discuss the importance and the use of the results developed in this paper.

DOI

10.1051/ro/2016026

Print ISSN

03990559

E-ISSN

12903868

Publisher Statement

Copyright © EDP Sciences, ROADEF, SMAI 2016. Access to external full text or publisher's version may require subscription.

Full-text Version

Publisher’s Version

Recommended Citation

Guo, X. & Wong, W.-K. (2016). Multivariate stochastic dominance for risk averters and risk seekers. RAIRO-Operation Research, 50(3), 575-586. doi: 10.1051/ro/2016026