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Robust Optimal Control for a Consumption-investment Problem

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  • Alexander Schied
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    Abstract

    We give an explicit PDE characterization for the solution of the problem of maximizing the utility of both terminal wealth and intertemporal consumption under model uncertainty. The underlying market model consists of a risky asset, whose volatility and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in terms of a HARA utility function with risk aversion parameter 0

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2007-026.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2007-026.

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    Length: 21
    Date of creation: May 2007
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2007-026

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    Related research

    Keywords: Optimal Consumption; Robust Control; Model Uncertainty; Incomplete Markets; Stochastic Volatility; Coherent Risk Measures; Convex Duality;

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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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. Daniel Hernandez–Hernandez & Alexander Schied, 2006. "A Control Approach to Robust Utility Maximization with Logarithmic Utility and Time-Consistent Penalties," SFB 649 Discussion Papers SFB649DP2006-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Daniel Hernandez–Hernandez & Alexander Schied, 2005. "Robust Utility Maximization in a Stochastic Factor Model," SFB 649 Discussion Papers SFB649DP2006-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2006.
    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. Denis Talay & Ziyu Zheng, 2002. "Worst case model risk management," Finance and Stochastics, Springer, vol. 6(4), pages 517-537.
    6. 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.
    7. Hernández-Hernández Daniel & Schied Alexander, 2006. "Robust utility maximization in a stochastic factor model," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 24(1/2006), pages 17, July.
    8. Alexander Schied, 2005. "Optimal Investments for Risk- and Ambiguity-Averse Preferences: A Duality Approach," SFB 649 Discussion Papers SFB649DP2005-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2006.
    9. Burgert Christian & Rüschendorf Ludger, 2005. "Optimal consumption strategies under model uncertainty," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 23(1/2005), pages 1-14, January.
    10. Ralf Korn & Olaf Menkens, 2005. "Worst-Case Scenario Portfolio Optimization: a New Stochastic Control Approach," Computational Statistics, Springer, Springer, vol. 62(1), pages 123-140, 09.
    11. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, 04.
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    Citations

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    Cited by:
    1. Volodymyr Perederiy, 2007. "Kombinierte Liquiditäts- und Solvenzkennzahlen und ein darauf basierendes Insolvenzprognosemodell für deutsche GmbHs," SFB 649 Discussion Papers SFB649DP2007-060, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.

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