dc.contributor.author Bouchard, Bruno dc.date.accessioned 2009-09-09T13:53:38Z dc.date.available 2009-09-09T13:53:38Z dc.date.issued 2005 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/1529 dc.language.iso en en dc.subject Partial order en dc.subject Probability en dc.subject Bipolar theorem en dc.subject Convex analysis en dc.subject.ddc 519 en dc.title A version of the G-conditionial bipolar theorem in L0(Rd;P) en dc.type Article accepté pour publication ou publié dc.description.abstracten Motivated by applications in financial mathematics, Ref. 3 showed that, although $$L^{0}(\mathbb{R}_{+}; \Omega, {\cal F}, \mathbb{P})$$ fails to be locally convex, an analogue to the classical bipolar theorem can be obtained for subsets of $$L^{0}(\mathbb{R}_{+}; \Omega, {\cal F}, \mathbb{P})$$ : if we place this space in polarity with itself, the bipolar of a set of non-negative random variables is equal to its closed (in probability), solid, convex hull. This result was extended by Ref. 1 in the multidimensional case, replacing $$\mathbb{R}_{+}$$ by a closed convex cone K of [0, infin)d, and by Ref. 12 who provided a conditional version in the unidimensional case. In this paper, we show that the conditional bipolar theorem of Ref. 12 can be extended to the multidimensional case. Using a decomposition result obtained in Ref. 3 and Ref. 1, we also remove the boundedness assumption of Ref. 12 in the one dimensional case and provide less restrictive assumptions in the multidimensional case. These assumptions are completely removed in the case of polyhedral cones K. en dc.relation.isversionofjnlname Journal of Theoretical Probability dc.relation.isversionofjnlvol 18 en dc.relation.isversionofjnlissue 2 en dc.relation.isversionofjnldate 2005 dc.relation.isversionofjnlpages 439-467 en dc.relation.isversionofdoi http://dx.doi.org/10.1007/s10959-005-3512-y en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Springer en dc.subject.ddclabel Probabilités et mathématiques appliquées en
﻿

## Files in this item

FilesSizeFormatView

There are no files associated with this item.