Matrix-Variate Value-at-Risk: Generalized Beta and F Distributions

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dc.contributor.affiliationArias-Serna, M.-A., Faculty of Engineering, Faculty of Basic Sciences, University of Medellin, Medellin, Colombia
dc.contributor.affiliationCaro-Lopera, F.J., Faculty of Engineering, Faculty of Basic Sciences, University of Medellin, Medellin, Colombia
dc.contributor.affiliationLoubes, J.-M., Institut de Mathématiques de Toulouse, University of Toulouse, Toulouse, France
dc.contributor.authorArias-Serna M.-A
dc.contributor.authorCaro-Lopera F.J
dc.contributor.authorLoubes J.-M.
dc.date.accessioned2025-04-28T22:10:54Z
dc.date.available2025-04-28T22:10:54Z
dc.date.issued2025
dc.descriptionIn 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.
dc.identifier.doi10.1080/01966324.2024.2443831
dc.identifier.instnameinstname:Universidad de Medellínspa
dc.identifier.issn1966324
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellínspa
dc.identifier.repourlrepourl:https://repository.udem.edu.co/
dc.identifier.urihttps://hdl.handle.net/11407/8911
dc.language.isoeng
dc.publisherTaylor and Francis Ltd.spa
dc.publisher.facultyFacultad de Ingenieríasspa
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.publisher.programIngeniería Financieraspa
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85215523006&doi=10.1080%2f01966324.2024.2443831&partnerID=40&md5=7609c733fe75b8b75b1deb0336f9a7c0
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dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.sourceAmerican Journal of Mathematical and Management Sciences
dc.sourceAm J Math Manage Sci
dc.sourceScopus
dc.subjectBeta-Kotz distribution
dc.subjectGauss hypergeometric function
dc.subjectGeneralized beta and F distributions
dc.subjectMatrix lower Value-at-Risk
dc.subjectMatrix upper Value-at-Risk
dc.subjectZonal polynomials
dc.subjectDistribution functions
dc.subjectMatrix algebra
dc.subjectPolynomials
dc.subjectRisk assessment
dc.subjectRisk management
dc.subjectBeta-kotz distribution
dc.subjectF distribution
dc.subjectGauss hypergeometric function
dc.subjectGeneralized beta distribution
dc.subjectmatrix
dc.subjectMatrix low value-at-risk
dc.subjectMatrix upper value-at-risk
dc.subjectValue at Risk
dc.subjectZonal polynomials
dc.subjectGaussian distribution
dc.subjectBeta-Kotz distribution
dc.subjectGauss hypergeometric function
dc.subjectGeneralized beta and F distributions
dc.subjectMatrix lower Value-at-Risk
dc.subjectMatrix upper Value-at-Risk
dc.subjectZonal polynomials
dc.titleMatrix-Variate Value-at-Risk: Generalized Beta and F Distributions
dc.typeArticle
dc.type.localArtículo revisado por paresspa
dc.type.versioninfo:eu-repo/semantics/publishedVersion

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