Open AccessTail risk measures with application for mixtures of elliptical distributions
Author(s) -
Pingyun Li,
Chuancun Yin
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022491
Subject(s) - multivariate statistics , portfolio , class (philosophy) , scale (ratio) , mathematics , variance (accounting) , focus (optics) , distribution (mathematics) , decomposition , pure mathematics , statistics , chemistry , physics , mathematical analysis , computer science , economics , artificial intelligence , optics , financial economics , accounting , quantum mechanics , organic chemistry
In this paper we derive explicit formulas of tail conditional expectation ($ \text{TCE} $) and tail variance ($ \text{TV} $) for the class of location-scale mixtures of elliptical distributions, which includes the generalized hyper-elliptical ($ \text{GHE} $) distribution. We also develop portfolio risk decomposition with $ \text{TCE} $ for multivariate location-scale mixtures of elliptical distributions. To illustrate our findings, we focus on the generalized hyperbolic ($ \text{GH} $) family which is a popular subclass of the $ \text{GHE} $ for stocks modelling.