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Inf-Convolution, Optimal Allocations, and Model Uncertainty for Tail Risk Measures

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 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 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.

Ketersediaan

Informasi Detail

Judul Seri

MATHEMATICS OF OPERATIONS RESEARCH; Vol.47 No.3 August 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2494-2519

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

PARETO OPTIMALITY
VALUE AT RISK
NONCONVEX OPTIMIZATION
RISK SHARING
RANGE VALUE AT RISK

Info Detail Spesifik

https://doi.org/10.1287/moor.2021.1217

Pernyataan Tanggungjawab

Fangda Liu, Tiantian Mao, Ruodu Wang, Linxiao Wei

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