Bilateral risk sharing in a comonotone market with rank-dependent utilities
研究了两个等级依赖效用最大化者在共单调市场中的双边风险分担问题，通过变分法刻画最优风险分配，并利用无约束问题的元素最大化者将损失支撑集划分为不相交片段，揭示每个片段上的显式结构。
This paper studies a bilateral risk-sharing problem in which the two agents are rank-dependent utility maximizers, and the market restricts risk allocations to be comonotonic. We first characterize the optimal risk allocation in an implicit way through the calculus of variations. Then, based on the element-wise maximizer of an unconstrained problem, we partition the support of loss into disjoint pieces and unveil the explicit structure of the optimal risk allocation over each piece. Our methodology reduces the dimension of the problem. We show the applicability of our results via two examples in which both agents use exponential utilities and use convex power or inverse-S-shaped probability weighting functions.<br/><br/>