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On Admissible Strategies in Robust Utility Maximization

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  • Keita Owari

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 "good definition" of admissible strategies, so that an optimizer is obtained. Under suitable assumptions, especially a time-consistency property of the set of probabilities which describes the model uncertainty, we show that an optimal strategy is obtained in the class of strategies whose wealths are supermartingales under all local martingale measures having a finite generalized entropy with at least one of candidate models (probabilities).

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  • Keita Owari, 2011. "On Admissible Strategies in Robust Utility Maximization," Papers 1109.5512, arXiv.org, revised Mar 2012.
  • Handle: RePEc:arx:papers:1109.5512
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    File URL: http://arxiv.org/pdf/1109.5512
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Yuri M. Kabanov & Christophe Stricker, 2002. "On the optimal portfolio for the exponential utility maximization: remarks to the six-author paper," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 125-134.
    7. Keita Owari, 2011. "A Note on Utility Maximization with Unbounded Random Endowment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(1), pages 89-103, March.
    8. Keita Owari, 2011. "Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem," Papers 1101.2968, arXiv.org.
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    Cited by:

    1. Keita Owari, 2013. "A Robust Version of Convex Integral Functionals," Papers 1305.6023, arXiv.org, revised May 2015.

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