风险分担、变异性度量与扭曲风险度量
Risk sharing, measuring variability, and distortion riskmetrics
AI总结：
本文针对一般扭曲风险度量下的风险分担问题，刻画了帕累托最优配置，并显式求解了基于基尼偏差、均值-中位数偏差及分位数间差的最优配置，发现后者呈现反单调混合结构。
摘要：
我们研究了在偏好由一类一般的共单调可加且基于律的函数所建模的代理人之间分担风险的问题，这类函数不必是单调的或凸的。这类函数被称为扭曲风险度量，其中包括投资组合优化和保险中使用的许多风险与变异性统计度量。在各种一般或共单调风险分担问题的设置下，我们刻画了帕累托最优配置的集合。我们使用基尼偏差、均值-中位数偏差或分位数间差作为相关的变异性度量，显式求解了代理人之间的帕累托最优配置。后者尤其引人关注，因为在存在分位数间差代理人的情况下，最优配置不是共单调的；相反，最优配置具有成对反单调结构的混合特征，显示出极值负依赖的某些模式。
英文摘要：
We address the problem of sharing risk among agents with preferences modelled by a general class of comonotonic additive and law-based functionals that need not be either monotone or convex. Such functionals are called distortion riskmetrics, which include many statistical measures of risk and variability used in portfolio optimization and insurance. The set of Pareto-optimal allocations is characterized under various settings of general or comonotonic risk sharing problems. We solve explicitly Pareto-optimal allocations among agents using the Gini deviation, the mean-median deviation, or the inter-quantile difference as the relevant variability measures. The latter is of particular interest, as optimal allocations are not comonotonic in the presence of inter-quantile difference agents; instead, the optimal allocation features a mixture of pairwise counter-monotonic structures, showing some patterns of extremal negative dependence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
