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

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Author Info
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
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Publisher 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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Find related papers by 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

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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.:
  1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  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. [Downloadable!]
  4. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November. [Downloadable!] (restricted)
    Other versions:
  5. Lars Peter Hansen & Thomas J. Sargent, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Quantitative Finance Papers math/0407127, arXiv.org. [Downloadable!]
  8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  9. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2004. "Dynamic monetary risk measures for bounded discrete-time processes," Quantitative Finance Papers math/0410453, arXiv.org. [Downloadable!]
  10. Volker Krätschmer, 2005. "Robust representation of convex risk measures by probability measures," Finance and Stochastics, Springer, vol. 9(4), pages 597-608, October. [Downloadable!] (restricted)
  11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  12. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522_v1, HAL. [Downloadable!]
  13. Denis Talay & Ziyu Zheng, 2002. "Worst case model risk management," Finance and Stochastics, Springer, vol. 6(4), pages 517-537. [Downloadable!] (restricted)
  14. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447. [Downloadable!] (restricted)
    Other versions:
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Cited by:
(explanations, 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.)

  1. 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. [Downloadable!]
  2. Anja Schöttner, 2005. "Relational Contracts and Job Design," SFB 649 Discussion Papers SFB649DP2005-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  3. 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. [Downloadable!]
  4. Alejandro Balbás & Raquel Balbás, 2009. "Compatibility between pricing rules and risk measures: The CCVaR," Business Economics Working Papers wb090201, Universidad Carlos III, Departamento de Economía de la Empresa. [Downloadable!]
  5. Alexander Schied, 2007. "Robust Optimal Control for a Consumption-investment Problem," SFB 649 Discussion Papers SFB649DP2007-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  6. Alejandro Balbas, 2008. "Capital requirements: Are they the best solution?," Business Economics Working Papers wb087114, Universidad Carlos III, Departamento de Economía de la Empresa. [Downloadable!]
  7. Yasemin Boztug & Lutz Hildebrandt, 2005. "An empirical test of theories of price valuation using a semiparametric approach, reference prices, and accounting for heterogeneity," SFB 649 Discussion Papers SFB649DP2005-057, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  8. Christian Weiner, 2005. "The Impact of Industry Classification Schemes on Financial Research," SFB 649 Discussion Papers SFB649DP2005-062, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  9. Wiebke Wittmüß, 2006. "Robust Optimization of Consumption with Random Endowment," SFB 649 Discussion Papers SFB649DP2006-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  10. Xiaoxian Ma & Qingzhen Zhao & Jilin Qu, 2008. "Robust portfolio optimization with a generalized expected utility model under ambiguity," Annals of Finance, Springer, vol. 4(4), pages 431-444, October. [Downloadable!] (restricted)
  11. Wolfgang Härdle & Sigbert Klinke & Uwe Ziegenhagen, 2005. "Integrable e-lements for Statistics Education," SFB 649 Discussion Papers SFB649DP2005-058, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  12. Imen Bentahar & Bruno Bouchard, 2005. "Explicit characterization of the super-replication strategy in financial markets with partial transaction costs," SFB 649 Discussion Papers SFB649DP2005-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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