A Robust Version of Convex Integral Functionals

Keita Owari
Additional contact information
Keita Owari: The University of Tokyo

No CARF-F-319, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: We consider the pointwise supremum of a family of convex integral functionals of essentially bounded random variables, each associated to a common convex integrand and a respective probability measure belonging to a dominated weakly compact convex set. Its conjugate functional is analyzed, providing a pair of upper and lower bounds as direct sums of common regular part and respective singular parts, which coincide when the defining set of probabilities is a singleton, as the classical Rockafellar theorem, and these bounds are generally the best in a certain sense. We then investigate when the conjugate eliminates the singular measures, which a fortiori implies the equality of the upper and lower bounds, and its relation to other finer regularity properties of the original functional and of the conjugate. As an application, a general duality result in the robust utility maximization problem is obtained.

Pages: 27 pages
Date: 2013-05
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (1)

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Related works:
Working Paper: A Robust Version of Convex Integral Functionals (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf319

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