<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Fangda Liu</style></author><author><style face="normal" font="default" size="100%">Tiantian Mao</style></author><author><style face="normal" font="default" size="100%">Ruodu Wang</style></author><author><style face="normal" font="default" size="100%">Linxiao Wei</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Inf-Convolution, Optimal Allocations, and Model Uncertainty for Tail Risk Measures</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics of Operations Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year><pub-dates><date><style  face="normal" font="default" size="100%">12 Sep 2021</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1287/moor.2021.1217</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">47</style></volume><pages><style face="normal" font="default" size="100%">2494-2519</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;
	Inspired by the recent developments in risk sharing problems for the value at&amp;nbsp;risk (VaR), the expected shortfall (ES), and the range value at risk (RVaR), we study the optimization&amp;nbsp;of risk sharing for general tail risk measures. Explicit formulas of the infconvolution&amp;nbsp;and Pareto-optimal allocations are obtained in the case of a mixed collection of&amp;nbsp;left and right VaRs, and in that of a VaR and another tail risk measure. The inf-convolution&amp;nbsp;of tail risk measures is shown to be a tail risk measure with an aggregated tail parameter, a&amp;nbsp;phenomenon very similar to the cases of VaR, ES, and RVaR. Optimal allocations are obtained&amp;nbsp;in the settings of elliptical models and model uncertainty. In particular, several results&amp;nbsp;are established for tail riskmeasures in the presence ofmodel uncertainty, which may&amp;nbsp;be of independent interest outside the framework of risk sharing. The technical conclusions&amp;nbsp;are quite general without assuming any form of convexity of the tail risk measures. Our&amp;nbsp;analysis generalizes in several directions the recent literature on quantile-based risk&amp;nbsp;sharing.
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