Publication: Stability in locally L0-convex modules and a conditional version of James' compactness theorem
Authors
Orihuela Calatayud, José ; Zapata García, José Miguel
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Publisher
Elsevier
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DOI
https://doi.org/10.1016/j.jmaa.2017.03.048
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info:eu-repo/semantics/article
Description
© 2017 Elsevier Inc. All rights reserved. This document is the Published version of a Published Work that appeared in final form in Journal of Mathematical Analysis and Applications. To access the final edited and published work see https://doi.org/10.1016/j.jmaa.2017.03.048
Abstract
Locally L0-convex modules were introduced in Filipovic et al. (2009) [10] as the analytic basis for the study of conditional risk measures. Later, the algebra of conditional sets was introduced in Drapeau et al. (2016) [8]. In this paper we study locally L0-convex modules, and find exactly which subclass of locally L0-convex modules can be identified with the class of locally convex vector spaces within the context of conditional set theory. Second, we provide a version of the classical James’ theorem of characterization of weak compactness for conditional Banach
spaces. Finally, we state a conditional version of the Fatou and Lebesgue properties for conditional convex risk measures and, as application of the developed theory, we establish a version of the so-called Jouini–Schachermayer–Touzi theorem for robust representation of conditional convex risk measures defined on a L∞-type module.
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Citation
J. Math. Anal. Appl. 452 (2017) 1101–1127
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