Stochastic orderings with respect to a capacity and an application to a financial optimization problem

Abstract : In an analogous way to the classical case of a probability measure, we extend the notion of an increasing convex (concave) stochastic dominance relation to the case of a normalised monotone (but not necessarily additive) set function also called a capacity. We give different characterizations of this relation establishing a link to the notions of distribution function and quantile function with respect to the given capacity. The Choquet integral is extensively used as a tool. We state a new version of the classical upper (resp. lower) Hardy-Littlewood's inequality generalized to the case of a continuous from below concave (resp. convex) capacity. We apply our results to a financial optimization problem whose constraints are expressed by means of the increasing convex stochastic dominance relation with respect to a capacity.
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https://hal.archives-ouvertes.fr/hal-00614716
Contributor : Miryana Grigorova <>
Submitted on : Monday, August 15, 2011 - 4:01:40 PM
Last modification on : Sunday, March 31, 2019 - 1:31:19 AM
Long-term archiving on: Friday, November 25, 2011 - 11:12:07 AM

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Miryana Grigorova. Stochastic orderings with respect to a capacity and an application to a financial optimization problem. 2011. ⟨hal-00614716⟩

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