Multivariate concave and convex stochastic dominance
AbstractStochastic 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.
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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2010044.
Date of creation: 01 Jul 2010
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decision analysis: multiple criteria; risk; group decisions; utility/preference: multiattribute utility; stochastic dominance; stochastic orders;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-12 (All new papers)
- NEP-SEA-2011-02-12 (South East Asia)
- NEP-UPT-2011-02-12 (Utility Models & Prospect Theory)
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