The average risk sharing problem under risk measure and expected utility theory

Abstract

In this paper, we investigate an average risk sharing problem, in which the optimal objective function is called an average-inf-convolution. We study the properties of the average-inf-convolution for a general risk measure, and obtain the explicit form of the average-inf-convolution. We also analyze the average risk sharing problems in the classic utility models in behavioral economics. Explicit forms of the average-inf-convolutions are obtained in the expected utility model and in the utility-based shortfall model, respectively. In the rank-dependent expected utility (RDEU) model, we give a lower bound of the average-inf-convolution for the RDEU-based shortfall.