@article{ea7c249425584ca6bd1d933d7dbb453e,
title = "Risk measures: A generalization from the univariate to the matrix-variate",
abstract = "This paper develops a method for estimating value-at-risk and conditional value-at-risk when the underlying risk factors follow a beta distribution in a univariate and a matrix-variate setting. For this purpose, we connect the theory of the Gaussian hypergeometric function of matrix argument and integration over positive definite matrixes. For certain choices of the shape parameters, a and b, analytical expressions of the risk measures are developed. More generally, a numerical solution for the risk measures for any parameterization of beta-distributed loss variables is presented. The proposed risk measures are finally used for quantifying the potential risk of economic loss in credit risk.",
keywords = "Beta distribution, Gaussian hypergeometric function of matrix argu-ment, Positive definite matrixes, Risk measures",
author = "Arias-Serna, {Mar{\'i}a A.} and Caro-Lopera, {Francisco J.} and Loubes, {Jean Michel}",
note = "Funding Information: This work was supported by the Doctoral School of Mathematics, IT and Telecommunications, University of Toulouse, France, and the Doctorate in Modelling and Scientific Computing of University of Medell?n, Colombia. Funding Information: The authors would like to thank the editor-in-chief and anonymous referees for careful reading and helpful suggestions. This work was supported by the Doctoral School of Mathematics, IT and Telecommunications, University of Toulouse, France, and the Doctorate in Modelling and Scientific Computing of University of Medell{\'i}n, Colombia. Publisher Copyright: {\textcopyright} 2021 Infopro Digital Risk (IP) Limited.",
year = "2021",
doi = "10.21314/JOR.2021.003",
language = "Ingl{\'e}s",
volume = "23",
pages = "1--20",
journal = "Journal of Risk",
issn = "1465-1211",
publisher = "Incisive Media Ltd.",
number = "4",
}