Risk sharing under heterogeneous beliefs without convexity
研究了在个体风险度量非凸且信念异质时，如何找到有限个代理人之间的帕累托最优风险分配，给出了一个简单的存在性条件。
Abstract We consider the problem of finding (Pareto-)optimal allocations of risk among finitely many agents. The associated individual risk measures are law-invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measures. Moreover, we assume that the individual risk assessments are consistent with the respective second-order stochastic dominance relations, but remain agnostic about their convexity. A simple sufficient condition for the existence of Pareto optima is provided. The proof combines local comonotonic improvement with a Dieudonné-type argument, which also establishes a link of the optimal allocation problem to the realm of “collapse to the mean” results.