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ON ADMISSIBLE STRATEGIES IN ROBUST UTILITY MAXIMIZATION (Forthcoming in "Mathematics and Financial Economics")

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  • Keita Owari

    (Faculty of Economics, University of Tokyo)

Abstract

The existence of optimal strategy in robust utility maximization is addressed when the utility function is finite on the entire real line. A delicate problem in this case is to find a ggood definitionh of admissible strategies to obtain an optimizer. Under certain assumptions, especially a time-consistency property of the set ‚o of probabilities which describes the model uncertainty, we show that an optimal strategy is obtained in the class of those whose wealths are supermartingales under all local martingale measures having a finite generalized entropy with one of P ¸ ‚o.

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File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/268.pdf
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Bibliographic Info

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-257.

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Length: 15 pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:cfi:fseres:cf257

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  1. 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.
  2. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
  3. Keita Owari, 2011. "A Note on Utility Maximization with Unbounded Random Endowment," Asia-Pacific Financial Markets, Springer, vol. 18(1), pages 89-103, March.
  4. 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.
  5. 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.
  6. Keita Owari, 2011. "Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem," Papers 1101.2968, arXiv.org.
  7. Sara Biagini & Marco Frittelli, 2007. "The supermartingale property of the optimal wealth process for general semimartingales," Finance and Stochastics, Springer, vol. 11(2), pages 253-266, April.
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