A Representation Result for Concave Schur Concave Functions
Sujetconcave rearrangement-invariant functions; law-invariant risk measures; law-invariant concave functions; concave Schur concave functions; second-order stochastic dominance; concave order
Journal issueMathematical Finance
MetadataShow full item record
Abstract (EN)A representation result is provided for concave Schur concave functions on L∞(Ω). In particular, it is proven that any monotone concave Schur concave weakly 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 law-invariant functions.
Showing items related by title, author, creator and subject.
Balabdaoui, Fadoua; Rufibach, Kaspar; Wellner, Jon (2009) Article accepté pour publication ou publié
A monotonic method for solving nonlinear optimal control problems with concave dependence on the state Salomon, Julien; Turinici, Gabriel (2011) Article accepté pour publication ou publié
Balabdaoui, Fadoua; Pitman, Jim (2011) Article accepté pour publication ou publié