Annals of Operations Research

, Volume 181, Issue 1, pp 325–335 | Cite as

Kusuoka representation of higher order dual risk measures

  • Darinka DentchevaEmail author
  • Spiridon Penev
  • Andrzej Ruszczyński


We derive representations of higher order dual measures of risk in Open image in new window 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.


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


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Darinka Dentcheva
    • 1
    Email author
  • Spiridon Penev
    • 2
  • Andrzej Ruszczyński
    • 3
  1. 1.Stevens Institute of TechnologyHobokenUSA
  2. 2.The University of New South WalesSydneyAustralia
  3. 3.Rutgers UniversityPiscatawayUSA

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