Kusuoka representation of higher order dual risk measures

Darinka Dentcheva, Spiridon Penev, Andrzej Ruszczynski

Research output: Contribution to journalArticle

16 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)325-335
Number of pages11
JournalAnnals of Operations Research
Volume181
Issue number1
DOIs
StatePublished - Dec 1 2010

Fingerprint

Risk measures
Measure of risk
Factors
Integral
Statistics
Distribution function
Value at risk

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

Cite this

Dentcheva, Darinka ; Penev, Spiridon ; Ruszczynski, Andrzej. / Kusuoka representation of higher order dual risk measures. In: Annals of Operations Research. 2010 ; Vol. 181, No. 1. pp. 325-335.
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Kusuoka representation of higher order dual risk measures. / Dentcheva, Darinka; Penev, Spiridon; Ruszczynski, Andrzej.

In: Annals of Operations Research, Vol. 181, No. 1, 01.12.2010, p. 325-335.

Research output: Contribution to journalArticle

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