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Infinitely many securities and the fundamental theorem of asset pricing

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dc.affiliation.dptoUC3M. Departamento de Economía de la Empresaes
dc.contributor.authorBalbás, Alejandro
dc.contributor.authorDownarowicz, Anna
dc.date.accessioned2012-01-16T18:21:09Z
dc.date.available2012-01-16T18:21:09Z
dc.date.issued2007-10
dc.description.abstractSeveral authors have pointed out the possible absence of martingale measures for static arbitrage free markets with an infinite number of available securities. Accordingly, the literature constructs martingale measures by generalizing the concept of arbitrage (free lunch, free lunch with bounded risk, etc.) or introducing the theory of large financial markets. This paper does not modify the definition of arbitrage and addresses the caveat by drawing on projective systems of probability measures. Thus we analyze those situations for which one can provide a projective system of σ−additive measures whose projective limit may be interpreted as a risk-neutral probability of an arbitrage free market. Hence the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets.
dc.description.sponsorshipPartially funded by the Spanish Ministry of Science and Education (ref: BEC2003 − 09067 − C04 − 03) and Comunidad Autónoma de Madrid (ref: s − 0505/tic/000230).
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationMediterranean Journal of Mathematics, 2007, v. 4, nº 3, pp. 321-341
dc.identifier.doi10.1007/s00009-007-0121-2
dc.identifier.issn1660-5446
dc.identifier.publicationfirstpage321
dc.identifier.publicationissue3
dc.identifier.publicationlastpage341
dc.identifier.publicationtitleMediterranean Journal of Mathematics
dc.identifier.publicationvolume4
dc.identifier.urihttps://hdl.handle.net/10016/12972
dc.language.isoeng
dc.publisherSpringer
dc.relation.isversionofhttp://e-archivo.uc3m.es/handle/10016/426
dc.relation.publisherversionhttp://dx.doi.org/10.1007/s00009-007-0121-2
dc.rights©Birkhäuser Verlag Basel
dc.rights.accessRightsopen access
dc.subject.ecienciaEmpresa
dc.subject.otherInfinitely many securities
dc.subject.otherArbitrage
dc.subject.otherMartingale measure
dc.subject.otherProjective system
dc.titleInfinitely many securities and the fundamental theorem of asset pricing
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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