dc.contributor.author Bouchard, Bruno dc.contributor.author Mazliak, Laurent dc.date.accessioned 2009-09-28T12:17:43Z dc.date.available 2009-09-28T12:17:43Z dc.date.issued 2003 dc.identifier.issn 0304-4149 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/2009 dc.language.iso en en dc.subject Convex analysis dc.subject Probability dc.subject.ddc 519 en dc.title A multidimensional bipolar theorem in L0(Rd;P) dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Université Pierre et Marie Curie, Paris;France dc.description.abstracten In 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.isversionofjnlname Stochastic Processes and their Applications dc.relation.isversionofjnlvol 107 dc.relation.isversionofjnlissue 2 dc.relation.isversionofjnldate 2003 dc.relation.isversionofjnlpages 213-231 dc.relation.isversionofdoi http://dx.doi.org/10.1016/S0304-4149(03)00073-5 dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Elsevier dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.description.ssrncandidate non dc.description.halcandidate oui dc.description.readership recherche dc.description.audience International dc.relation.Isversionofjnlpeerreviewed oui dc.date.updated 2020-05-20T04:46:26Z
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