On Admissible Strategies in Robust Utility Maximization
AbstractThe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1109.5512.
Date of creation: Sep 2011
Date of revision: Mar 2012
Publication status: Published in Mathematics and Financial Economics, Vol. 6, No. 2, pp. 77-92, 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-09 (All new papers)
- NEP-MIC-2011-10-09 (Microeconomics)
- NEP-UPT-2011-10-09 (Utility Models & Prospect Theory)
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- Sara Biagini & Marco Frittelli, 2007. "The supermartingale property of the optimal wealth process for general semimartingales," Finance and Stochastics, Springer, Springer, vol. 11(2), pages 253-266, April.
- Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, Springer, vol. 11(1), pages 107-129, January.
- 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.
- Keita Owari, 2011. "Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem," Papers 1101.2968, arXiv.org.
- Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, Springer, vol. 5(4), pages 557-581.
- Schied Alexander & Wu Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 23(3/2005), pages 199-217, March.
- Keita Owari, 2009.
"A Note on Utility Maximization with Unbounded Random Endowment,"
Global COE Hi-Stat Discussion Paper Series, Institute of Economic Research, Hitotsubashi University
gd09-091, Institute of Economic Research, Hitotsubashi University.
- Keita Owari, 2011. "A Note on Utility Maximization with Unbounded Random Endowment," Asia-Pacific Financial Markets, Springer, Springer, vol. 18(1), pages 89-103, March.
- 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, Wiley Blackwell, vol. 12(2), pages 125-134.
- Keita Owari, 2013.
"A Robust Version of Convex Integral Functionals,"
1305.6023, arXiv.org, revised Jun 2014.
- Keita Owari, 2013. "A Robust Version of Convex Integral Functionals," CARF F-Series, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo CARF-F-319, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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