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Robust Exponential Hedging And Indifference Valuation

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  • KEITA OWARI

    ()
    (Graduate School of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8601, Japan)

Abstract

We discuss the problem of exponential hedging in the presence of model uncertainty expressed by a set of probability measures. This is a robust utility maximization problem with a contingent claim. We first consider the dual problem which is the minimization of penalized relative entropy over a product set of probability measures, showing the existence and variational characterizations of the solution. These results are applied to the primal problem. Then we consider the robust version of exponential utility indifference valuation, giving the representation of indifference price using a duality result.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 13 (2010)
Issue (Month): 07 ()
Pages: 1075-1101

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Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:07:p:1075-1101

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Keywords: Model uncertainty; duality; utility maximization; hedging;

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  1. 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.
  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.
  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. Hernández-Hernández, Daniel & Schied, Alexander, 2007. "A control approach to robust utility maximization with logarithmic utility and time-consistent penalties," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 980-1000, August.
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Cited by:
  1. Keita Owari, 2009. "A Note on Utility Maximization with Unbounded Random Endowment," Global COE Hi-Stat Discussion Paper Series gd09-091, Institute of Economic Research, Hitotsubashi University.

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