Matrix-variate risk measures under Wishart and gamma distributions

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dc.contributor.affiliationFaculty of Engineering, University of Medellin, Medellin, Colombia
dc.contributor.affiliationFaculty of Basic Sciences, University of Medellin, Medellin, Colombia
dc.contributor.affiliationInstitut 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.accessioned2025-12-03T19:34:51Z
dc.date.available2025-12-03T19:34:51Z
dc.date.issued2025
dc.descriptionMatrix-variate distribution theory has been instrumental across various disciplines for the past seven decades. However, a comprehensive examination of financial literature reveals a notable gap concerning the application of matrix-variate extensions to Value-at-Risk (VaR). However, from a mathematical perspective, the core requirement for VaR lies in determining meaningful percentiles within the context of finance, necessitating the consideration of matrix c.d.f. This paper introduces the concept of “matrix-variate VaR” for both Wishart and Gamma distributions. To achieve this, we leverage the theory of hypergeometric functions of matrix argument and integrate over positive definite matrices. Our proposed approach adeptly characterizes a company's exposure by into a comprehensive risk measure. This facilitates a readily computable estimation of the total incurred risk. Notably, this approach enables efficient computation of risk measures under Wishart, exponential, Erlang, gamma, and chi-square distributions. The resulting risk measures are expressed in closed analytic forms, enhancing their practical utility for day-to-day risk management. © 2024 Wiley Periodicals LLC.
dc.identifier.doi10.1002/jcaf.22734
dc.identifier.instnameinstname:Universidad de Medellínspa
dc.identifier.issn10448136
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellínspa
dc.identifier.repourlrepourl:https://repository.udem.edu.co/
dc.identifier.urihttp://hdl.handle.net/11407/9266
dc.language.isoeng
dc.publisherJohn Wiley and Sons Incspa
dc.publisher.facultyFacultad de Ingenierías-Instituto de Ciencias Básicasspa
dc.publisher.programIngeniería Financieraspa
dc.relation.citationendpage23
dc.relation.citationissue1
dc.relation.citationstartpage9
dc.relation.citationvolume36
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85195088219&doi=10.1002%2fjcaf.22734&partnerID=40&md5=bf290650604223dcb1d5389cdad762b3
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dc.rights.accesoRestricted access
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.sourceJournal of Corporate Accounting and Finance
dc.sourceJ. corp. account. finance
dc.sourceScopus
dc.subjectGeneralized Wishart distribution
dc.subjectHypergeometric function of matrix argument
dc.subjectJames' Zonal polynomials
dc.subjectMatrix-variate VaR
dc.subjectPositive definite matrices
dc.subjectRisk measures
dc.titleMatrix-variate risk measures under Wishart and gamma distributions
dc.typeArticle
dc.type.localArtículospa
dc.type.versioninfo:eu-repo/semantics/publishedVersion

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