A directional multivariate value at risk

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dc.citation.journalTitleINSURANCE MATHEMATICS & ECONOMICSeng
dc.contributor.authorTorres, R.
dc.contributor.authorLillo, R.E.
dc.contributor.authorLaniado, H.
dc.contributor.departmentUniversidad EAFIT. Escuela de Cienciasspa
dc.contributor.researchgroupModelado Matemáticospa
dc.date.accessioned2021-04-12T14:07:10Z
dc.date.available2021-04-12T14:07:10Z
dc.date.issued2015-11-01
dc.description.abstractIn economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability alpha, the 100 alpha% VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is alpha. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretation as a risk measure. However, its extension to the multivariate framework is not unique because a unique definition of multivariate quantile does not exist. In the current literature, the multivariate quantiles are related to a specific partial order considered in R-n, or to a property of the univariate quantile that is desirable to be extended to R-n. In this work, we introduce a multivariate value at risk as a vector-valued directional risk measure, based on a directional multivariate quantile, which has recently been introduced in the literature. The directional approach allows the manager to consider external information or risk preferences in her/his analysis. We derive some properties of the risk measure and we compare the univariate VaR over the marginals with the components of the directional multivariate VaR. We also analyze the relationship between some families of copulas, for which it is possible to obtain closed forms of the multivariate VaR that we propose. Finally, comparisons with other alternative multivariate VaR given in the literature, are provided in terms of robustness. (C) 2015 Elsevier B.V. All rights reserved.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1751
dc.identifier.doi10.1016/j.insmatheco.2015.09.002
dc.identifier.issn01676687
dc.identifier.issn18735959
dc.identifier.otherWOS;000367109800013
dc.identifier.otherSCOPUS;2-s2.0-84944044478
dc.identifier.urihttp://hdl.handle.net/10784/27760
dc.language.isoengeng
dc.publisherElsevier
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84944044478&doi=10.1016%2fj.insmatheco.2015.09.002&partnerID=40&md5=d69e7f94ebfaf9b1e8e4dc957a7f6695
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0167-6687
dc.sourceINSURANCE MATHEMATICS & ECONOMICS
dc.subject.keywordMultivariate riskseng
dc.subject.keywordValue at riskeng
dc.subject.keywordDirectional approacheng
dc.subject.keywordMultivariate quantileeng
dc.subject.keywordCopulaeng
dc.titleA directional multivariate value at riskeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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