The Average Risk Sharing Problem Based On Risk Measures

We build a new type of risk sharing model called average risk sharing problem and call the optimal objective function average-inf-convolution in the paper.We investigate the properties of average-inf-convolution for a general risk measure,and explicitly find the answer,which is the largest risk measure satisfying convexity and dominated by the original risk measure.We also apply the average risk sharing problem to classic utili-ty models in behavior economic theory.For expected loss and utility-based shortfall,explicit forms of average-inf-convolution are obtained.In expected loss model,the an-swer is the expected loss with the largest convex loss function dominated by the original loss function.In utility-based shortfall model,the answer is the utility-based shortfall with the smallest concave utility function dominating the original utility function.For rank-dependent expected utility(RDEU)model,we only give a lower bound for the average-inf-convolution.The result in this paper corresponds to behavior economic models,and emphasis the importance of convex risk measure in avoiding regulatory arbitrage to some extent.