Risk Sharing, Measuring Variability, and Distortion Riskmetrics
研究了一类非单调非凸的扭曲风险度量下代理人之间的风险分担问题，给出了帕累托最优分配的特征，并针对基尼偏差、中位数偏差和分位数间差等变异性度量求解了显式最优分配。
ABSTRACT We address the problem of sharing risk among agents with preferences modeled by a general class of comonotonic additive and law‐invariant 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 interquantile difference (IQD) as the relevant variability measures. The latter is of particular interest, as optimal allocations are not comonotonic in the presence of IQD agents; instead, the optimal allocation features a mixture of pairwise counter‐monotonic structures, showing some patterns of extremal negative dependence.