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Minimizing measures of risk by saddle point conditions

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dc.affiliation.dptoUC3M. Departamento de Economía de la Empresaes
dc.contributor.authorBalbás, Alejandro
dc.contributor.authorBalbás, Beatriz
dc.contributor.authorBalbás, Raquel
dc.date.accessioned2012-01-16T19:14:20Z
dc.date.available2012-01-16T19:14:20Z
dc.date.issued2010-09
dc.description.abstractThe minimization of risk functions is becoming a very important topic due to its interesting applications in Mathematical Finance and Actuarial Mathematics. This paper addresses this issue in a general framework. Many types of risk function may be involved. A general representation theorem of risk functions is used in order to transform the initial optimization problem into an equivalent one that overcomes several mathematical caveats of risk functions. This new problem involves Banach spaces but a mean value theorem for risk measures is stated, and this simplifies the dual problem. Then, optimality is characterized by saddle point properties of a bilinear expression involving the primal and the dual variable. This characterization is significantly different if one compares it with previous literature. Furthermore, the saddle point condition very easily applies in practice. Four applications in finance and insurance are presented.en
dc.description.sponsorshipThis research was partially supported by ‘‘Welzia Management SGIIC SA, RD_Sistemas SA’’ and ‘‘MEyC’’ (Spain), Grant ECO2009-14457-C04.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Computational and applied mathematics, 2010, v. 234, nº 10, pp. 2924-2931en
dc.identifier.doi10.1016/j.cam.2010.04.002
dc.identifier.issn0377-0427
dc.identifier.publicationfirstpage2924
dc.identifier.publicationissue10
dc.identifier.publicationlastpage2931
dc.identifier.publicationtitleJournal of Computational and applied mathematicsen
dc.identifier.publicationvolume234
dc.identifier.urihttps://hdl.handle.net/10016/12974
dc.language.isoeng
dc.publisherElsevier
dc.relation.projectIDComunidad de Madrid. S2009/ESP-1685/RIESGOSes
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.cam.2010.04.002
dc.rights.accessRightsopen access
dc.subject.ecienciaEmpresa
dc.subject.otherRisk minimizationen
dc.subject.otherSaddle point conditionen
dc.subject.otherActuarial and finantial aplicationsen
dc.titleMinimizing measures of risk by saddle point conditionsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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