Stochastic dominance with respect to a capacity and risk measures - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

Stochastic dominance with respect to a capacity and risk measures

Résumé

Pursuing our previous work in which the classical notion of increasing convex stochastic dominance relation with respect to a probability has been extended to the case of a normalised monotone (but not necessarily additive) set function also called a capacity, the present paper gives a generalization to the case of a capacity of the classical notion of increasing stochastic dominance relation. This relation is characterized by using the notions of distribution function and quantile function with respect to the given capacity. Characterizations, involving Choquet integrals with respect to a distorted capacity, are established for the classes of monetary risk measures (defined on the space of bounded real-valued measurable functions) satisfying the properties of comonotonic additivity and consistency with respect to a given generalized stochastic dominance relation. Moreover, under suitable assumptions, a "Kusuoka-type" characterization is proved for the class of monetary risk measures having the properties of comonotonic additivity and consistency with respect to the generalized increasing convex stochastic dominance relation. Generalizations to the case of a capacity of some well-known risk measures (such as the Value at Risk or the Tail Value at Risk) are provided as examples. It is also established that some well-known results about Choquet integrals with respect to a distorted probability do not necessarily hold true in the more general case of a distorted capacity.
Fichier principal
Vignette du fichier
stochastic_orderings_and_risk_measures.pdf (432.04 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00639667 , version 1 (09-11-2011)

Identifiants

  • HAL Id : hal-00639667 , version 1

Citer

Miryana Grigorova. Stochastic dominance with respect to a capacity and risk measures. 2011. ⟨hal-00639667⟩
324 Consultations
591 Téléchargements

Partager

Gmail Facebook X LinkedIn More