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
Language
English
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