@article{Li2022, 
author = {Pingyun Li and Chuancun Yin},
title = {Tail risk measures with application for mixtures of elliptical distributions},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {8802-8821},
keywords = {tail conditional expectations, tail variance, portfolio risk decomposition with TCE, location-scale mixtures, elliptical distributions},
url = {https://www.sciopen.com/article/10.3934/math.2022491},
doi = {10.3934/math.2022491},
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.}
}