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Kusuoka Representation of Higher Order Dual Risk Measures

Darinka Dentcheva(darinka.dentcheva***at***stevens.edu)
Spiridon Penev(spiro***at***maths.unsw.edu.au)
Andrzej Ruszczynski(rusz***at***business.rutgers.edu)

Abstract: We derive representations of higher order dual measures of risk in $\mathcal{L}^p$ 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.

Keywords: Lorenz curve, quantile functions, average value at risk, coherent measures of risk, Fano factor, optimization, duality

Category 1: Stochastic Programming


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Entry Submitted: 03/24/2010
Entry Accepted: 03/25/2010
Entry Last Modified: 03/24/2010

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