TY - JOUR
T1 - Kusuoka representation of higher order dual risk measures
AU - Dentcheva, Darinka
AU - Penev, Spiridon
AU - Ruszczyński, Andrzej
PY - 2010/12
Y1 - 2010/12
N2 - 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.
AB - 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.
KW - Average value at risk
KW - Coherent measures of risk
KW - Duality
KW - Fano factor
KW - Lorenz curve
KW - Optimization
KW - Quantile functions
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U2 - 10.1007/s10479-010-0747-5
DO - 10.1007/s10479-010-0747-5
M3 - Article
AN - SCOPUS:78649798316
SN - 0254-5330
VL - 181
SP - 325
EP - 335
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 1
ER -