Inf-Convolution, Optimal Allocations, and Model Uncertainty for Tail Risk Measures
成果类型：
Article; Early Access
署名作者：
Liu, Fangda; Mao, Tiantian; Wang, Ruodu; Wei, Linxiao
署名单位：
University of Waterloo; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Wuhan University of Technology
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2021.1217
发表日期：
2022
关键词：
摘要：
Inspired by the recent developments in risk sharing problems for the value at risk (VaR), the expected shortfall (ES), and the range value at risk (RVaR), we study the optimization of risk sharing for general tail risk measures. Explicit formulas of the infconvolution 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 settings of elliptical models and model uncertainty. In particular, several results are established for tail risk measures in the presence of model uncertainty, which may be of independent interest outside the framework of risk sharing. 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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