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Risk measures: a generalization from the univariate to the matrix-variate

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Listed:
  • María A. Arias-Serna
  • Francisco J. Caro-Lopera
  • Jean-Michel Loubes

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.

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Handle: RePEc:rsk:journ4:7823146
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