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Kusuoka representation of higher order dual risk measures

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Abstract

We derive representations of higher order dual measures of risk in 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.

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Authors and Affiliations

  1. Stevens Institute of Technology, Hoboken, NJ, USA

    Darinka Dentcheva

  2. The University of New South Wales, Sydney, Australia

    Spiridon Penev

  3. Rutgers University, Piscataway, NJ, USA

    Andrzej Ruszczyński

Authors
  1. Darinka Dentcheva
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  2. Spiridon Penev
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  3. Andrzej Ruszczyński
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Correspondence to Darinka Dentcheva.

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Dentcheva, D., Penev, S. & Ruszczyński, A. Kusuoka representation of higher order dual risk measures. Ann Oper Res 181, 325–335 (2010). https://doi.org/10.1007/s10479-010-0747-5

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  • DOI: https://doi.org/10.1007/s10479-010-0747-5

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