Multivariate Concave and Convex Stochastic Dominance

28 Pages Posted: 23 Apr 2010

See all articles by Michel Denuit

Michel Denuit

Catholic University of Louvain

Louis Eeckhoudt

Catholic University of Lille - IESEG School of Management

Ilia Tsetlin


Robert L. Winkler

Duke University - Fuqua School of Business

Date Written: April 23, 2010


Stochastic dominance permits a partial ordering of alternatives (probability distributions on consequences) based only on partial information about a decision maker’s utility function. Univariate stochastic dominance has been widely studied and applied, with general agreement on classes of utility functions for dominance of different degrees. Extensions to the multivariate case have received less attention and have used different classes of utility functions, some of which require strong assumptions about utility. We investigate multivariate stochastic dominance using a class of utility functions that is consistent with a basic preference assumption, can be related to well-known characteristics of utility, and is a natural extension of the stochastic order typically used in the univariate case. These utility functions are multivariate risk averse, and reversing the preference assumption allows us to investigate stochastic dominance for utility functions that are multivariate risk seeking. We provide insight into these two contrasting forms of stochastic dominance, develop some criteria to compare probability distributions (hence alternatives) via multivariate stochastic dominance, and illustrate how this dominance could be used in practice to identify inferior alternatives. Connections between our approach and dominance using different stochastic orders are discussed.

Keywords: Decision Analysis, Multiple Criteria, Risk, Group Decisions, Utility/Preference, Multiattribute Utility, Stochastic Dominance, Stochastic Orders

Suggested Citation

Denuit, Michel and Eeckhoudt, Louis and Tsetlin, Ilia and Winkler, Robert L., Multivariate Concave and Convex Stochastic Dominance (April 23, 2010). INSEAD Working Paper No. 2010/29/DS, Available at SSRN: or

Michel Denuit (Contact Author)

Catholic University of Louvain ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348

Louis Eeckhoudt

Catholic University of Lille - IESEG School of Management ( email )

3 Rue de la Digue
Office: A321
Puteaux, 92800

Ilia Tsetlin

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex

Robert L. Winkler

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

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