Separation and Duality in Locally L0-Convex Modules

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.


Published in:
Journal of Functional Analysis, 256, 3996-4029
Year:
2009
ISSN:
0022-1236
Keywords:
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 Record created 2010-04-27, last modified 2018-03-17

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