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A Robust Version of Convex Integral Functionals

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  • Keita Owari

    (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.

Suggested Citation

  • Keita Owari, 2013. "A Robust Version of Convex Integral Functionals," CARF F-Series CARF-F-319, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf319
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    References listed on IDEAS

    as
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    Cited by:

    1. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.

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