Kusuoka representation of higher order dual risk measures

Darinka Dentcheva; Spiridon Penev; Andrzej Ruszczyński

doi:10.1007/s10479-010-0747-5

Kusuoka representation of higher order dual risk measures

Darinka Dentcheva
, Spiridon Penev
, Andrzej Ruszczyński

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We derive representations of higher order dual measures of risk in L^p spaces as suprema of integrals of Average Values at Risk with respect to probability measures on (0,1] (Kusuoka representations). The suprema are taken over convex sets of probability measures. The sets are described by constraints on the dual norms of certain transformations of distribution functions. For p=2, we obtain a special description of the set and we relate the measures of risk to the Fano factor in statistics.

Original language	English
Pages (from-to)	325-335
Number of pages	11
Journal	Annals of Operations Research
Volume	181
Issue number	1
DOIs	https://doi.org/10.1007/s10479-010-0747-5
State	Published - Dec 2010

Keywords

Average value at risk
Coherent measures of risk
Duality
Fano factor
Lorenz curve
Optimization
Quantile functions

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10.1007/s10479-010-0747-5

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AU - Penev, Spiridon

AU - Ruszczyński, Andrzej

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AB - We derive representations of higher order dual measures of risk in Lp spaces as suprema of integrals of Average Values at Risk with respect to probability measures on (0,1] (Kusuoka representations). The suprema are taken over convex sets of probability measures. The sets are described by constraints on the dual norms of certain transformations of distribution functions. For p=2, we obtain a special description of the set and we relate the measures of risk to the Fano factor in statistics.

KW - Average value at risk

KW - Coherent measures of risk

KW - Duality

KW - Fano factor

KW - Lorenz curve

KW - Optimization

KW - Quantile functions

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SP - 325

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JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 1

ER -

Kusuoka representation of higher order dual risk measures

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Keywords

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