Multivariate Concave and Convex Stochastic Dominance
28 Pages Posted: 23 Apr 2010
Date Written: April 23, 2010
Abstract
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: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
A Good Sign for Multivariate Risk Taking
By Louis Eeckhoudt, Béatrice Rey, ...
-
Apportioning of Risks via Stochastic Dominance
By Louis Eeckhoudt, Harris Schlesinger, ...
-
On the Precautionary Motive for Savings and Prudence, in an EU and a Neu Framework
By Eric Langlais, Alain Chateauneuf, ...
-
Comparative Ross Risk Aversion in the Presence of Mean Dependent Risks
By Georges Dionne and Jingyuan Li
-
By Yannick Malevergne and Béatrice Rey
-
Risk Apportionment and Stochastic Dominance
By Louis Eeckhoudt, Harris Schlesinger, ...