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Duality theory for optimal investments under model uncertainty

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Author Info
Alexander Schied
Ching-Tang Wu

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Abstract

Robust utility functionals arise as numerical representations of investor preferences, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In this paper, we study the duality theory for the problem of maximizing the robust utility of the terminal wealth in a general incomplete market model. We also allow for very general sets of prior models. In particular, we do not assume that all prior models are equivalent to each other, which allows us to handle many economically meaningful robust utility functionals such as those defined by AVaR(lambda), concave distortions, or convex capacities. We also show that dropping the equivalence of prior models may lead to new effects such as the existence of arbitrage strategies under the least favorable model.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2005-025.pdf
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File Function: Revised version, 2005
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Publisher Info
Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-025.

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Length: 22 pages
Date of creation: Feb 2005
Date of revision: Sep 2005
Handle: RePEc:hum:wpaper:sfb649dp2005-025

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Related research
Keywords: model uncertainty duality theory investment uncertainty utility arbitrage

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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. 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)
  2. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February. [Downloadable!] (restricted)
  3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  4. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581. [Downloadable!] (restricted)
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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. Markus Fischer & Markus Reiss, 2005. "Discretisation of Stochastic Control Problems for Continuous Time Dynamics with Delay," SFB 649 Discussion Papers SFB649DP2005-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Dec 2005. [Downloadable!]
  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. Anja Schöttner, 2005. "Relational Contracts and Job Design," SFB 649 Discussion Papers SFB649DP2005-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  4. Markus Krätzig, 2005. "A Software Framework for Data Based Analysis," SFB 649 Discussion Papers SFB649DP2005-044, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  5. Andreas Schabert & Christian Stoltenberg, 2005. "Money Demand and Macroeconomic Stability Revisited," SFB 649 Discussion Papers SFB649DP2005-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2005. [Downloadable!]
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  6. Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2005. "Portfolio Value at Risk Based on Independent Components Analysis," SFB 649 Discussion Papers SFB649DP2005-060, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  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. [Downloadable!]
  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. [Downloadable!]
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  9. Ajit Ghose, 2005. "Employment in China: Recent trends and future challenges," Employment strategy papers 2005-14, International Labour Office. [Downloadable!]
  10. María Echart, 2003. "Educación universitaria Aportes para el debate acerca de su efectividad y equidad," Working Papers 79, FIEL. [Downloadable!]
  11. Francesco Daveri & Cecilia Jona-Lasinio, . "Italy’s Decline: Getting the Facts Right," Working Papers 301, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
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  12. Alexander Schied, 2007. "Robust Optimal Control for a Consumption-investment Problem," SFB 649 Discussion Papers SFB649DP2007-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  13. Benjamin Bental & Dominique Demougin, 2005. "Do Factor Shares Reflect Technology?," SFB 649 Discussion Papers SFB649DP2005-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  14. 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!]
  15. 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!]
  16. Yasemin Boztug & Lutz Hildebrandt, 2005. "A Market Basket Analysis Conducted with a Multivariate Logit Model," SFB 649 Discussion Papers SFB649DP2005-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  17. Astrid Matthey, 2005. "Getting Used to Risks: Reference Dependence and Risk Inclusion," SFB 649 Discussion Papers SFB649DP2005-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  18. 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!]
  19. 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!]
  20. Anja Schöttner, 2005. "Fixed-Prize Tournaments versus First-Price Auctions in Innovation Contests," SFB 649 Discussion Papers SFB649DP2005-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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