## Publication: Differential equations connecting VaR and CVaR

 dc.affiliation.instituto UC3M. Instituto para el Desarrollo de Empresas y Mercados (INDEM) es dc.contributor.author Balbás, Alejandro dc.contributor.author Balbás, Beatriz dc.contributor.author Balbás, Raquel dc.contributor.editor Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial es dc.contributor.other es dc.date.accessioned 2017-01-10T12:51:11Z dc.date.available 2017-01-10T12:51:11Z dc.date.issued 2017-01-09 dc.description.abstract The 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.mimetype application/pdf dc.identifier.issn 1989-8843 es dc.identifier.uri https://hdl.handle.net/10016/24017 dc.identifier.uxxi DT/0000001499 es dc.language.iso eng es dc.relation.ispartofseries Working paper Business Economic Series en dc.relation.ispartofseries 17-01 es dc.rights Atribución-NoComercial-SinDerivadas 3.0 España dc.rights.accessRights open access en dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject.jel C65 es dc.subject.jel G11 es dc.subject.jel G12 es dc.subject.jel G22 es dc.subject.other VaR and CVaR en dc.subject.other Differential Equations en dc.subject.other VaR Representation Theorem en dc.subject.other Risk Optimization and Probabilistic Constraints en dc.subject.other Risk and Marginal Risk Estimation en dc.title Differential equations connecting VaR and CVaR en dc.type working paper * dc.type.hasVersion AO * dspace.entity.type Publication
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