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Proceedings of the American Mathematical Society

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A pointwise bipolar theorem


Authors: Daniel Bartl and Michael Kupper
Journal: Proc. Amer. Math. Soc. 147 (2019), 1483-1495
MSC (2010): Primary 46N10, 46N30, 91G10
DOI: https://doi.org/10.1090/proc/14231
Published electronically: December 31, 2018
MathSciNet review: 3910414
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Abstract: We provide a pointwise bipolar theorem for $\liminf$-closed convex sets of positive Borel measurable functions on a $\sigma$-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a version of the transport duality under nontight marginals, and a superhedging duality for semistatic hedging in discrete time.


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Additional Information

Daniel Bartl
Affiliation: Department of Mathematics, University of Konstanz, Universitätstra${\ss }$e 10, 78464, Konstanz, Germany
MR Author ID: 1186301
Email: daniel.bartl@uni-konstanz.de

Michael Kupper
Affiliation: Department of Mathematics, University of Konstanz, Universitätstra${\ss }$e 10, 78464, Konstanz, Germany
MR Author ID: 736016
Email: kupper@uni-konstanz.de

Keywords: Bipolar theorem, convex closed sets, duality, robust finance, transport duality, semistatic hedging
Received by editor(s): February 8, 2017
Received by editor(s) in revised form: May 18, 2018
Published electronically: December 31, 2018
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2018 American Mathematical Society