Core of convex distortions of a probability on a non atomic space

Abstract

his paper characterizes the core of a differentiable convex dis-tortion of a probability measure on a non atomic space by identifying it withthe set of densities which dominate the derivative of the distortion, for secondorder stochastic dominance. Furthermore the densities that have the samedistribution as the derivative of the distortion are the extreme points of thecore. These results are applied to the differentiability of a Choquet integralwith respect to a distortion of a probability measure (respectively the dif-ferentiability of a Yaari’s or Rank Dependent Expected utility function). AChoquet integral is differentiable atxif and only ifxhas a strictly increasingquantile function. The superdifferential of a Choquet integral at any point isthen fully characterized. Examples of uses of these results in simple modelswhere some agent is a Rank Dependent Expected Utility (RDEU) maximizerare then given. In particular, efficient risk sharing among an expected utilitymaximizer and a RDEU maximizer and among two RDEU maximizers ischaracterized

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