Kusuoka representation of higher order dual risk measures

Darinka Dentcheva, Spiridon Penev, Andrzej Ruszczyński

Research output: Contribution to journalArticle

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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

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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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