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Optimal Investments for Risk- and Ambiguity-Averse Preferences: A Duality Approach

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  • Alexander Schied
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    Abstract

    Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling. A recent paper by Maccheroni et al. (2004) characterizes investor preferences under aversion against both risk and ambiguity. Their result shows that these preferences can be numerically represented in terms of convex risk measures. In this paper we study the corresponding problem of optimal investment over a given time horizon, using a duality approach and building upon the results by Kramkov and Schachermayer (1999, 2001).

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2005-051.pdf
    File Function: Revised version, 2006
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-051.

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    Length: 27 pages
    Date of creation: Sep 2005
    Date of revision: Aug 2006
    Handle: RePEc:hum:wpaper:sfb649dp2005-051

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    Related research

    Keywords: Model uncertainty; ambiguity; convex risk measures; optimal investments; duality theory;

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    References

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    1. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    2. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    3. 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.
    4. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    5. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    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. Burgert Christian & Rüschendorf Ludger, 2005. "Optimal consumption strategies under model uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 1-14, January.
    8. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    9. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2004. "Dynamic monetary risk measures for bounded discrete-time processes," Papers math/0410453, arXiv.org.
    10. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    11. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    12. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    13. 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.
    14. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127, arXiv.org.
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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. 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. Wiebke Wittmüß, 2006. "Robust Optimization of Consumption with Random Endowment," SFB 649 Discussion Papers SFB649DP2006-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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