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Separation and duality in locally L0-convex modules

Type of Publication: Journal article
Publication status: Published
Author: Filipović, Damir; Kupper, Michael; Vogelpoth, Nicolas
Year of publication: 2009
Published in: Journal of Functional Analysis ; 256 (2009), 12. - pp. 3996-4029. - ISSN 0022-1236. - eISSN 1096-0783
DOI (citable link): https://dx.doi.org/10.1016/j.jfa.2008.11.015
Summary:
Motivated by financial applications, we study convex analysis for modules over the ordered ring L0 of random variables. We establish a module analogue of locally convex vector spaces, namely locally L0-convex modules. In this context, we prove hyperplane separation theorems. We investigate continuity, subdifferentiability and dual representations of Fenchel–Moreau type for L0-convex functions from L0-modules into L0. Several examples and applications are given.
Subject (DDC): 510 Mathematics

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FILIPOVIĆ, Damir, Michael KUPPER, Nicolas VOGELPOTH, 2009. Separation and duality in locally L0-convex modules. In: Journal of Functional Analysis. 256(12), pp. 3996-4029. ISSN 0022-1236. eISSN 1096-0783. Available under: doi: 10.1016/j.jfa.2008.11.015

@article{Filipovic2009-06Separ-40942, title={Separation and duality in locally L0-convex modules}, year={2009}, doi={10.1016/j.jfa.2008.11.015}, number={12}, volume={256}, issn={0022-1236}, journal={Journal of Functional Analysis}, pages={3996--4029}, author={Filipović, Damir and Kupper, Michael and Vogelpoth, Nicolas} }

2017-12-14T09:04:48Z Filipović, Damir Vogelpoth, Nicolas Kupper, Michael Separation and duality in locally L<sup>0</sup>-convex modules Motivated by financial applications, we study convex analysis for modules over the ordered ring L<sup>0</sup> of random variables. We establish a module analogue of locally convex vector spaces, namely locally L<sup>0</sup>-convex modules. In this context, we prove hyperplane separation theorems. We investigate continuity, subdifferentiability and dual representations of Fenchel–Moreau type for L<sup>0</sup>-convex functions from L<sup>0</sup>-modules into L<sup>0</sup>. Several examples and applications are given. Vogelpoth, Nicolas Kupper, Michael eng Filipović, Damir 2017-12-14T09:04:48Z 2009-06

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