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. The multivariate concave stochastic dominance we investigate is a natural extension of the stochastic order typically used in the univariate case and is consistent with a basic preference assumption. The corresponding 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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Acknowledgements
We thank the referee and Editor for many helpful comments. The financial support of the “Onderzoeksfonds K.U. Leuven” (GOA/07: Risk Modeling and Valuation of Insurance and Financial Cash Flows, with Applications to Pricing, Provisioning, and Solvency) is gratefully acknowledged by Michel Denuit. Ilia Tsetlin was supported in part by the INSEAD Alumni Fund.
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Denuit, M., Eeckhoudt, L., Tsetlin, I., Winkler, R.L. (2013). Multivariate Concave and Convex Stochastic Dominance. In: Biagini, F., Richter, A., Schlesinger, H. (eds) Risk Measures and Attitudes. EAA Series. Springer, London. https://doi.org/10.1007/978-1-4471-4926-2_2
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