- Kusuoka Representation of Higher Order Dual Risk Measures Darinka Dentcheva(darinka.dentchevastevens.edu) Spiridon Penev(spiromaths.unsw.edu.au) Andrzej Ruszczynski(ruszbusiness.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 Citation: Download: [PDF]Entry Submitted: 03/24/2010Entry Accepted: 03/25/2010Entry Last Modified: 03/24/2010Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society.