Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : A representation result is provided for concave Schur concave functions on L∞( ). In particular, it is proven that any monotone concave Schur concaveweakly upper semicontinuous function is the infinimum of a family of nonnegative affine combinations of Choquet integrals with respect to a convex continuous distortion of the underlying probability. The method of proof is based on the concave Fenchel transform and on Hardy and Littlewood’s inequality. Under the assumption that the probability space is nonatomic, concave, weakly upper semicontinuous, law-invariant functions are shown to coincide with weakly upper semicontinuous concave Schur concave functions. A representation result is, thus, obtained for weakly upper semicontinuous concave lawinvariant functions.
DANA Rose-Anne
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
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