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

Author

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  • Miryana Grigorova

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Miryana Grigorova, 2011. "Stochastic orderings with respect to a capacity and an application to a financial optimization problem," Working Papers hal-00614716, HAL.
    • Handle: RePEc:hal:wpaper:hal-00614716
    Note: View the original document on HAL open archive server: https://hal.science/hal-00614716
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