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
Contributeur : Miryana Grigorova <>
Soumis le : lundi 15 août 2011 - 16:01:40
Dernière modification le : mercredi 12 octobre 2016 - 01:02:10
Document(s) archivé(s) le : vendredi 25 novembre 2011 - 11:12:07

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  • HAL Id : hal-00614716, version 1

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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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