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Research Article | Open Access

Tail risk measures with application for mixtures of elliptical distributions

Pingyun Li, Chuancun Yin( )
School of Statistics and Data Science, Qufu Normal University, Qufu, Shandong 273165, China
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Abstract

In this paper we derive explicit formulas of tail conditional expectation ( TCE) and tail variance ( TV) for the class of location-scale mixtures of elliptical distributions, which includes the generalized hyper-elliptical ( GHE) distribution. We also develop portfolio risk decomposition with TCE for multivariate location-scale mixtures of elliptical distributions. To illustrate our findings, we focus on the generalized hyperbolic ( GH) family which is a popular subclass of the GHE for stocks modelling.

Keywords

tail conditional expectationstail varianceportfolio risk decomposition with TCElocation-scale mixtureselliptical distributions
CLC number: 62E10, 62H05

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8802-8821
DOI: 10.3934/math.2022491

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Li P, Yin C. Tail risk measures with application for mixtures of elliptical distributions. AIMS Mathematics, 2022, 7(5): 8802-8821. https://doi.org/10.3934/math.2022491

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Received: 10 August 2021
Revised: 22 February 2022
Accepted: 23 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)