Stochastic orderings with respect to a capacity and an application to a financial optimization problem
| Autor: | Miryana Grigorova |
|---|---|
| Přispěvatelé: | Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Grigorova, Miryana |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
stochastic orderings increasing convex stochastic dominance Choquet integral quantile function with respect to a capacity stop-loss ordering Choquet expected utility distorted capacity generalized Hardy-Littlewood's inequalities distortion risk measure ambiguity Mathematical optimization [MATH.MATH-PR] Mathematics [math]/Probability [math.PR] generalized Hardy-Littlewood's inequalities Logarithmically concave function Stochastic dominance increasing convex stochastic dominance [QFIN.RM]Quantitative Finance [q-fin]/Risk Management [q-fin.RM] [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP] [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] quantile function with respect to a capacity Distortion risk measure Applied mathematics [QFIN.RM] Quantitative Finance [q-fin]/Risk Management [q-fin.RM] ComputingMilieux_MISCELLANEOUS Probability measure Mathematics [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP] [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Quantile function [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Monotone polygon stop-loss ordering Choquet integral Set function Modeling and Simulation distortion risk measure ambiguity Statistics Probability and Uncertainty stochastic orderings distorted capacity Choquet expected utility |
| Zdroj: | Statistics & Risk Modeling with Applications in Finance and Insurance Statistics & Risk Modeling with Applications in Finance and Insurance, De Gruyter, 2014, 31 (2), pp.183-213 Statistics & Risk Modeling with Applications in Finance and Insurance, 2014, 31 (2), pp.183-213 |
| ISSN: | 2196-7040 |
| Popis: | By analogy with the classical case of a probability measure, we extend the notion of increasing convex (concave) stochastic dominance relation to the case of a normalized 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. In the second part of the paper, we give an application to a financial optimization problem whose constraints are expressed by means of the increasing convex stochastic dominance relation with respect to a capacity. The problem is solved by using, among other tools, a result established in our previous work, namely 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. The value function of the optimization problem is interpreted in terms of risk measures (or premium principles). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|