Publication:
Martingales and Arbitrage: a new look

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dc.affiliation.dptoUC3M. Departamento de Economía de la Empresaes
dc.contributor.authorBalbás, Alejandro
dc.contributor.authorJimenez Guerra, Pedro
dc.date.accessioned2014-01-20T16:04:28Z
dc.date.available2014-01-20T16:04:28Z
dc.date.issued2009-06
dc.description.abstractThis paper addresses the equivalence between the absence of arbitrage and the existence of equivalent martingale measures. The equivalence will be established under quite weak assumptions since there are no conditions on the set of trading dates (it may be finite or countable, with bounded or unbounded horizon, etc.) or on the trajectories of the price process (for instance, they do not have to be right-continuous). Besides we will deal with arbitrage portfolios rather than free-lunches. The concept of arbitrage is much more intuitive than the concept of free lunch and has more clear economic interpretation. Furthermore it is more easily tested in theoretical models or practical applications. In order to overcome the usual mathematical difficulties arising when dealing with arbitrage strategies, the set of states of nature will be widened by drawing on projective systems of Radon probability measures, whose projective limit will be the martingale measure. The existence of densities between the "real" probabilities and the "risk-neutral" probabilities will be guaranteed by introducing the concept of "projective equivalence". Hence some classical counter-examples will be solved and a complete characterization of the absence of arbitrage will be provided in a very general framework.en
dc.description.sponsorshipResearch partially supported by “Comunidad Autónoma de Madrid” (Spain), Grant s-0505/tic/000230, and “MEyC” (Spain), Grant SEJ2006-15401-C04en
dc.description.statusPublicadoes
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas (RACSAM), 2009, v. 103, n. 2, pp. 265-275es
dc.identifier.issn1578-7303
dc.identifier.publicationfirstpage265
dc.identifier.publicationissue2
dc.identifier.publicationlastpage275
dc.identifier.publicationtitleRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticases
dc.identifier.publicationvolume103
dc.identifier.urihttps://hdl.handle.net/10016/18152
dc.identifier.uxxiAR/0000006595
dc.language.isoenges
dc.publisherSpringeren
dc.relation.isversionofhttp://hdl.handle.net/10016/137
dc.relation.publisherversionhttp://dx.doi.org/10.1007/BF03191907
dc.rightsSpringeren
dc.rights.accessRightsopen accessen
dc.subject.otherArbitrageen
dc.subject.otherMartingale measureen
dc.subject.otherProjective systemen
dc.titleMartingales and Arbitrage: a new looken
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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