Kusuoka representation of higher order dual risk measures

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.

• Type: Journal
• Year: 2010
• Where: ANOR
• Authors: Darinka Dentcheva, Spiridon Penev, Andrzej Ruszczynski
• Keywords: ANOR 2010, Convex Sets, Neural Networks, Order Dual Measures, Probability Measures