Kusuoka representation of higher order dual risk measures

Darinka Dentcheva, Spiridon Penev, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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
Issue number1
StatePublished - Dec 2010

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research


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


Dive into the research topics of 'Kusuoka representation of higher order dual risk measures'. Together they form a unique fingerprint.

Cite this