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

Rutgers Business School, Management & Information Systems

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

21 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 (US)
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

All Science Journal Classification (ASJC) codes

Decision Sciences(all)
Management Science and Operations Research

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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title = "Kusuoka representation of higher order dual risk measures",

abstract = "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.",

keywords = "Average value at risk, Coherent measures of risk, Duality, Fano factor, Lorenz curve, Optimization, Quantile functions",

author = "Darinka Dentcheva and Spiridon Penev and Andrzej Ruszczy{\'n}ski",

note = "Funding Information: Acknowledgements The first author was partially by the NSF grant DMS-0604060. The second author was partially supported by a research grant PS15611 of The University of New South Wales. The third author was partially supported by the NSF grant DMS-0603728.",

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AU - Dentcheva, Darinka

AU - Penev, Spiridon

AU - Ruszczyński, Andrzej

N1 - Funding Information: Acknowledgements The first author was partially by the NSF grant DMS-0604060. The second author was partially supported by a research grant PS15611 of The University of New South Wales. The third author was partially supported by the NSF grant DMS-0603728.

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N2 - 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.

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

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KW - Duality

KW - Fano factor

KW - Lorenz curve

KW - Optimization

KW - Quantile functions

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Kusuoka representation of higher order dual risk measures

Abstract

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