• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

A version of the G-conditionial bipolar theorem in L0(Rd;P)

Thumbnail
Date
2005
Dewey
Probabilités et mathématiques appliquées
Sujet
Partial order; Probability; Bipolar theorem; Convex analysis
Journal issue
Journal of Theoretical Probability
Volume
18
Number
2
Publication date
2005
Article pages
439-467
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10959-005-3512-y
URI
https://basepub.dauphine.fr/handle/123456789/1529
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Bouchard, Bruno
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.