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Robust Utility Maximization in a Stochastic Factor Model

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  • Daniel Hernandez–Hernandez
  • Alexander Schied

Abstract

We give an explicit PDE characterization for the solution of a robust utility maximization problem in an incomplete market model, whose volatility, interest rate process, 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 negative risk aversion and a dynamically consistent coherent risk measure, which allows for model uncertainty in the distributions of both the asset price dynamics and the factor process. Our method combines two recent advances in the theory of optimal investments: the general duality theory for robust utility maximization and the stochastic control approach to the dual problem of determining optimal martingale measures.

Suggested Citation

  • 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.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-007
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-007.pdf
    File Function: Revised version, 2006
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    References listed on IDEAS

    as
    1. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    2. 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.
    3. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    5. 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.
    6. 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.
    7. 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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    Citations

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    Cited by:

    1. Alexander Schied, 2007. "Robust Optimal Control for a Consumption-investment Problem," SFB 649 Discussion Papers SFB649DP2007-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. 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.
    3. Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.
    4. Wiebke Wittmüß, 2006. "Robust Optimization of Consumption with Random Endowment," SFB 649 Discussion Papers SFB649DP2006-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Owari, Keita, 2008. "Robust Exponential Hedging and Indifference Valuation," Discussion Papers 2008-09, Graduate School of Economics, Hitotsubashi University.
    6. Keita Owari, 2009. "Robust Exponential Hedging in a Brownian Setting," Global COE Hi-Stat Discussion Paper Series gd09-082, Institute of Economic Research, Hitotsubashi University.
    7. 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.
    8. Daniel Hernández-Hernández & Alexander Schied, 2007. "Robust Maximization of Consumption with Logarithmic Utility," SFB 649 Discussion Papers SFB649DP2007-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    optimal investment; model uncertainty; incomplete markets; stochastic volatility; coherent risk measures; optimal control; convex duality;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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