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Differential equations connecting VaR and CVaR

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dc.affiliation.institutoUC3M. Instituto para el Desarrollo de Empresas y Mercados (INDEM)es
dc.contributor.authorBalbás, Alejandro
dc.contributor.authorBalbás, Beatriz
dc.contributor.authorBalbás, Raquel
dc.contributor.editorUniversidad Carlos III de Madrid. Instituto para el Desarrollo Empresariales
dc.contributor.otheres
dc.date.accessioned2017-01-10T12:51:11Z
dc.date.available2017-01-10T12:51:11Z
dc.date.issued2017-01-09
dc.description.abstractThe Value at Risk (VaR) is a very important risk measure for practitioners, supervisors and researchers. Many practitioners draw on VaR as a critical instrument in Risk Management and other Actuarial/Financial problems, while super- visors and regulators must deal with VaR due to the Basel Accords and Solvency II, among other reasons. From a theoretical point of view VaR presents some drawbacks overcome by other risk measures such as the Conditional Value at Risk (CVaR). VaR is neither differentiable nor sub-additive because it is neither continuous nor convex. On the contrary, CVaR satis es all of these properties, and this simpli es many ana- lytical studies if VaR is replaced by CVaR. In this paper several differential equations connecting both VaR and CVaR will be presented. They will allow us to address several important issues involving VaR with the help of the CVaR properties. This new methodology seems to be very efficient. In particular, a new VaR Representation Theorem may be found, and optimization problems involving VaR or probabilistic constraints always have an equivalent differentiable optimization problem. Applications in VaR, marginal VaR, CVaR and marginal CVaR estimates will be addressed as well. An illustrative actuarial numerical example will be given.en
dc.format.mimetypeapplication/pdf
dc.identifier.issn1989-8843es
dc.identifier.urihttps://hdl.handle.net/10016/24017
dc.identifier.uxxiDT/0000001499es
dc.language.isoenges
dc.relation.ispartofseriesWorking paper Business Economic Seriesen
dc.relation.ispartofseries17-01es
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.jelC65es
dc.subject.jelG11es
dc.subject.jelG12es
dc.subject.jelG22es
dc.subject.otherVaR and CVaRen
dc.subject.otherDifferential Equationsen
dc.subject.otherVaR Representation Theoremen
dc.subject.otherRisk Optimization and Probabilistic Constraintsen
dc.subject.otherRisk and Marginal Risk Estimationen
dc.titleDifferential equations connecting VaR and CVaRen
dc.typeworking paper*
dc.type.hasVersionAO*
dspace.entity.typePublication
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