Show simple item record

dc.contributor.authorBouchard, Bruno
dc.contributor.authorMazliak, Laurent
dc.date.accessioned2009-09-28T12:17:43Z
dc.date.available2009-09-28T12:17:43Z
dc.date.issued2003
dc.identifier.issn0304-4149
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/2009
dc.language.isoenen
dc.subjectConvex analysis
dc.subjectProbability
dc.subject.ddc519en
dc.titleA multidimensional bipolar theorem in L0(Rd;P)
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversité Pierre et Marie Curie, Paris;France
dc.description.abstractenIn this paper, we prove a multidimensional extension of the so-called Bipolar Theorem proved in Brannath and Schachermayer (Séminaire de Probabilités, vol. XXX, 1999, p. 349), which says that the bipolar of a convex set of positive random variables is equal to its closed, solid convex hull. This result may be seen as an extension of the classical statement that the bipolar of a subset in a locally convex vector space equals its convex hull. The proof in Brannath and Schachermayer (ibidem) is strongly dependent on the order properties of Image . Here, we define a (partial) order structure with respect to a d-dimensional convex cone K of the positive orthant [0,∞)d. We may then use compactness properties to work with the first component and obtain the result for convex subsets of K-valued random variables from the theorem of Brannath and Schachermayer (ibidem). As a byproduct, we obtain an equivalence property for a class of minimization problems in the spirit of Kramkov and Schachermayer (Ann. Appl. Probab 9(3) (1999) 904, Proposition 3.2). Finally, we discuss some applications in the context of duality theory of the utility maximization problem in financial markets with proportional transaction costs.
dc.relation.isversionofjnlnameStochastic Processes and their Applications
dc.relation.isversionofjnlvol107
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2003
dc.relation.isversionofjnlpages213-231
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/S0304-4149(03)00073-5
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-05-20T04:46:26Z


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record