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A Robust Version of Convex Integral Functionals

  • Keita Owari

    (The University of Tokyo)

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.

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Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-319.

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Length: 27 pages
Date of creation: May 2013
Date of revision:
Handle: RePEc:cfi:fseres:cf319
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  1. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
  2. Keita Owari, 2009. "A Note on Utility Maximization with Unbounded Random Endowment," Global COE Hi-Stat Discussion Paper Series gd09-091, Institute of Economic Research, Hitotsubashi University.
  3. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489,
  4. Alexander Schied & Ching-Tang Wu, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers SFB649DP2005-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Sep 2005.
  5. Keita Owari, 2011. "On Admissible Strategies in Robust Utility Maximization," Papers 1109.5512,, revised Mar 2012.
  6. Hernández-Hernández Daniel & Schied Alexander, 2006. "Robust utility maximization in a stochastic factor model," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 17, July.
  7. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
  8. Schied Alexander & Wu Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 23(3/2005), pages 199-217, March.
  9. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276.
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