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Duality theory for optimal investments under model uncertainty

  • Alexander Schied
  • Ching-Tang Wu
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    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
    File Function: Revised version, 2005
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    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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    Web page: http://sfb649.wiwi.hu-berlin.de
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    1. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar.
    2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    3. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    4. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    5. 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.
    6. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2007. "Optimal Risk Sharing for Law Invariant Monetary Utility Functions," Working Papers halshs-00176606, HAL.
    7. 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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