Matrix-Variate Value-at-Risk: Generalized Beta and F Distributions
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Taylor and Francis Ltd.
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In recent years, there has been a notable increase in the study of matrix-variate distributions and their applications. Significant progress has been made in understanding the properties and statistical inference of these distributions. In this paper, we introduce two alternative extensions of the univariate Value-at-Risk (VaR) within a matrix-variate context: the matrix upper VaR and the matrix lower VaR. These extensions are obtained as the zeroes of the Gauss hypergeometric function with a matrix argument, thereby providing valuable tools for risk assessment in a variety of fields, particularly in finance and capital allocation. In this paper, we provide the univariate VaR for the generalized beta and F distributions, as well as the matrix-variate VaR for these distributions. Moreover, we derive the beta-Kotz VaR based on a general family of distributions, which includes the classical Gaussian model. Furthermore, new integrals and results involving zonal polynomials are derived. This paper advances the understanding of matrix-variate VaR extensions, opening new avenues for their application in various disciplines. By bridging the gap between matrix-variate distributions and VaR, we aim to stimulate further research and practical implementations in financial risk management and capital optimization. © 2025 The Author(s). Published with license by Taylor & Francis Group, LLC.
Palabras clave
Beta-Kotz distribution, Gauss hypergeometric function, Generalized beta and F distributions, Matrix lower Value-at-Risk, Matrix upper Value-at-Risk, Zonal polynomials, Distribution functions, Matrix algebra, Polynomials, Risk assessment, Risk management, Beta-kotz distribution, F distribution, Gauss hypergeometric function, Generalized beta distribution, matrix, Matrix low value-at-risk, Matrix upper value-at-risk, Value at Risk, Zonal polynomials, Gaussian distribution, Beta-Kotz distribution, Gauss hypergeometric function, Generalized beta and F distributions, Matrix lower Value-at-Risk, Matrix upper Value-at-Risk, Zonal polynomials