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Robust optimal control for a consumption-investment problem

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  • Schied, Alexander

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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  • Schied, Alexander, 2007. "Robust optimal control for a consumption-investment problem," SFB 649 Discussion Papers 2007-026, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2007-026
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    References listed on IDEAS

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    1. Wittmüß, Wiebke, 2006. "Robust optimization of consumption with random endowment," SFB 649 Discussion Papers 2006-063, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. Hernández-Hernández Daniel & Schied Alexander, 2006. "Robust utility maximization in a stochastic factor model," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-17, July.
    3. Schied, Alexander, 2005. "Optimal investments for risk- and ambiguity-averse preferences: A duality approach," SFB 649 Discussion Papers 2005-051, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Ralf Korn & Olaf Menkens, 2005. "Worst-Case Scenario Portfolio Optimization: a New Stochastic Control Approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 123-140, September.
    5. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. 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.
    8. Schied, Alexander & Wu, Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers 2005-025, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. Denis Talay & Ziyu Zheng, 2002. "Worst case model risk management," Finance and Stochastics, Springer, vol. 6(4), pages 517-537.
    10. Alexander Schied, 2005. "Optimal Investments for Robust Utility Functionals in Complete Market Models," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 750-764, August.
    11. Schied Alexander & Wu Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 23(3), pages 199-217, March.
    12. Hernández-Hernández, Daniel & Schied, Alexander, 2006. "A control approach to robust utility maximization with logarithmic utility and time-consistent penalties," SFB 649 Discussion Papers 2006-061, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Ralf Korn & Paul Wilmott, 2002. "Optimal Portfolios Under The Threat Of A Crash," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 171-187.
    14. Hernández-Hernández, Daniel & Schied, Alexander, 2005. "Robust utility maximization in a stochastic factor model," SFB 649 Discussion Papers 2006-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Burgert Christian & Rüschendorf Ludger, 2005. "Optimal consumption strategies under model uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 1-14, January.
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    2. Perederiy, Volodymyr, 2007. "Kombinierte Liquiditäts- und Solvenzkennzahlen und ein darauf basierendes Insolvenzprognosemodell für deutsche GmbHs," SFB 649 Discussion Papers 2007-060, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.

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