@article {31119,
	title = {Inf-Convolution, Optimal Allocations, and Model Uncertainty for Tail Risk Measures},
	journal = {Mathematics of Operations Research},
	volume = {47},
	year = {2022},
	month = {12 Sep 2021},
	pages = {2494-2519},
	abstract = {<p>
	Inspired by the recent developments in risk sharing problems for the value at\&nbsp;risk (VaR), the expected shortfall (ES), and the range value at risk (RVaR), we study the optimization\&nbsp;of risk sharing for general tail risk measures. Explicit formulas of the infconvolution\&nbsp;and Pareto-optimal allocations are obtained in the case of a mixed collection of\&nbsp;left and right VaRs, and in that of a VaR and another tail risk measure. The inf-convolution\&nbsp;of tail risk measures is shown to be a tail risk measure with an aggregated tail parameter, a\&nbsp;phenomenon very similar to the cases of VaR, ES, and RVaR. Optimal allocations are obtained\&nbsp;in the settings of elliptical models and model uncertainty. In particular, several results\&nbsp;are established for tail riskmeasures in the presence ofmodel uncertainty, which may\&nbsp;be of independent interest outside the framework of risk sharing. The technical conclusions\&nbsp;are quite general without assuming any form of convexity of the tail risk measures. Our\&nbsp;analysis generalizes in several directions the recent literature on quantile-based risk\&nbsp;sharing.
</p>
},
	url = {https://doi.org/10.1287/moor.2021.1217},
	author = {Fangda Liu and Tiantian Mao and Ruodu Wang and Linxiao Wei}
}