Multivariate stochastic dominance for risk averters and risk seekers

Xu GUO, Wing-Keung WONG

Research output: Journal PublicationsJournal Article (refereed)

11 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)575-586
Number of pages12
JournalRAIRO-Operation Research
Volume50
Issue number3
DOIs
Publication statusPublished - 1 Jul 2016
Externally publishedYes

Fingerprint

Stochastic Dominance
Attribute
Stochastic dominance
Utility Maximization
Diversification
Expected Utility
Convex Combination
Random variables
Univariate
Random variable
Non-negative

Keywords

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

Cite this

GUO, Xu ; WONG, Wing-Keung. / Multivariate stochastic dominance for risk averters and risk seekers. In: RAIRO-Operation Research. 2016 ; Vol. 50, No. 3. pp. 575-586.
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Multivariate stochastic dominance for risk averters and risk seekers. / GUO, Xu; WONG, Wing-Keung.

In: RAIRO-Operation Research, Vol. 50, No. 3, 01.07.2016, p. 575-586.

Research output: Journal PublicationsJournal Article (refereed)

TY - JOUR

T1 - Multivariate stochastic dominance for risk averters and risk seekers

AU - GUO, Xu

AU - WONG, Wing-Keung

PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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.

AB - 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.

KW - Multivariate stochastic dominance

KW - ascending stochastic dominance

KW - descending stochastic dominance

KW - risk averters

KW - risk seekers

KW - utility function

UR - http://commons.ln.edu.hk/sw_master/5449

U2 - 10.1051/ro/2016026

DO - 10.1051/ro/2016026

M3 - Journal Article (refereed)

VL - 50

SP - 575

EP - 586

JO - RAIRO - Operations Research

JF - RAIRO - Operations Research

SN - 0399-0559

IS - 3

ER -