尾部风险测度的卷积与最优分配

Fangda Liu, Tiantian Mao, Ruodu Wang, Linxiao Wei
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引用次数: 4

摘要

受风险价值(VaR)、预期缺口(ES)和风险范围-价值(RVaR)的风险分担问题的启发,我们研究了一般尾部风险度量的风险分担优化问题。给出了左、右VaR混合集合和一个VaR与另一个尾部风险测度混合集合情况下的中卷积和pareto最优配置的显式公式。尾部风险测度的内卷积表现为尾部参数聚集的尾部风险测度,这一现象与VaR、ES和RVaR的情况非常相似。在椭圆模型设置下得到了最优分配,并对存在模型不确定性的尾部风险度量和风险分担问题得到了若干结果。技术结论是相当普遍的,没有假设任何形式的尾部风险措施的凸性。我们的分析从几个方面概括了最近关于基于分位数的风险分担的文献。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Inf-convolution and Optimal Allocations for Tail Risk Measures
Inspired by the recent developments in risk sharing problems for the Value-at-Risk (VaR), the Expected Shortfall (ES), or the Range-Value-at-Risk (RVaR), we study the optimization of risk sharing for general tail risk measures. Explicit formulas of the inf-convolution and Pareto-optimal allocations are obtained in the case of a mixed collection of left and right VaRs, and in that of a VaR and another tail risk measure. The inf-convolution of tail risk measures is shown to be a tail risk measure with an aggregated tail parameter, a phenomenon very similar to the cases of VaR , ES and RVaR. Optimal allocations are obtained in the setting of elliptical models,
and several results are established for tail risk measures and risk sharing problems in the presence of model uncertainty. The technical conclusions are quite general without assuming any form of convexity of the tail risk measures. Our analysis generalizes in several directions the recent literature on quantile-based risk sharing.
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