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Differentiability properties of Rank Linear Utilities, working paper CEREMADE, 2007-3, available at http://www.ceremade.dauphine.fr

By G. Carlier

Abstract

We study the differentiability properties of concave functionals defined as integrals of the quantile. These functionals generalize the rank dependent expected utility and are called rank-linear utilities in decision theory. Their superdifferential is described as well as the set of random variables where they are Gâteaux-differentiable. Our results generalize those obtained for the rank dependent expected utility in [1]

Year: 2013
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