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The Opportunity Process for Optimal Consumption and Investment with Power Utility

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  • Marcel Nutz
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    Abstract

    We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the resulting stochastic control problem. We show how the opportunity process describes the key objects: optimal strategy, value function, and dual problem. The results are applied to obtain monotonicity properties of the optimal consumption.

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    File URL: http://arxiv.org/pdf/0912.1879
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0912.1879.

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    Date of creation: Dec 2009
    Date of revision: Jun 2010
    Publication status: Published in Math. Financ. Econ., 3(3):139-159, 2010
    Handle: RePEc:arx:papers:0912.1879

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    Web page: http://arxiv.org/

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    1. Sasha F. Stoikov & Thaleia Zariphopoulou, 2005. "Dynamic Asset Allocation And Consumption Choice In Incomplete Markets ," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 414-454, December.
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    Cited by:
    1. Ulrich Horst & Ying Hu & Peter Imkeller & Anthony Reveillac, 2011. "Forward-backward systems for expected utility maximization," SFB 649 Discussion Papers SFB649DP2011-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Erhan Bayraktar & Ross Kravitz, 2011. "Stability of exponential utility maximization with respect to market perturbations," Papers 1107.2716, arXiv.org, revised Dec 2012.
    3. Horst, Ulrich & Hu, Ying & Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2014. "Forward–backward systems for expected utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1813-1848.
    4. Frei, Christoph & Mocha, Markus & Westray, Nicholas, 2012. "BSDEs in utility maximization with BMO market price of risk," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2486-2519.
    5. Markus Mocha & Nicholas Westray, 2011. "The Stability of the Constrained Utility Maximization Problem - A BSDE Approach," Papers 1107.0190, arXiv.org.
    6. Christoph Frei & Markus Mocha & Nicholas Westray, 2011. "BSDEs in Utility Maximization with BMO Market Price of Risk," Papers 1107.0183, arXiv.org, revised Feb 2012.
    7. Jan Kallsen & Johannes Muhle-Karbe & Richard Vierthauer, 2009. "Asymptotic Power Utility-Based Pricing and Hedging," Papers 0912.3362, arXiv.org, revised Jan 2013.

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