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Utility duality under additional information: Conditional measures versus filtration enlargements

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  • Ankirchner, Stefan

Abstract

The utility maximisation problem is considered for investors with anticipative additional information. We distinguish between models with conditional measures and models with enlarged filtrations. The dual functions of the maximal expected utility are determined with the help of f-divergences. We assume that our measures are absolutely continuous with respect to a local martingale measure (LMM), but not necessarily equivalent. Thus we do not exclude arbitrage.

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  • Ankirchner, Stefan, 2005. "Utility duality under additional information: Conditional measures versus filtration enlargements," SFB 649 Discussion Papers 2005-029, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2005-029
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    References listed on IDEAS

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    1. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    2. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
    3. José Mª Corcuera & Peter Imkeller & Arturo Kohatsu & David Nualart, 2003. "Additional utility of insiders with imperfect dynamical information," Economics Working Papers 675, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Ankirchner, Stefan & Dereich, Steffen & Imkeller, Peter, 2005. "The Shannon information of filtrations and the additional logarithmic utility of insiders," SFB 649 Discussion Papers 2005-030, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Martin Schweizer & Dirk Becherer & Jürgen Amendinger, 2003. "A monetary value for initial information in portfolio optimization," Finance and Stochastics, Springer, vol. 7(1), pages 29-46.
    6. Duffie, Darrell & Huang, Chi-fu, 1986. "Multiperiod security markets with differential information : Martingales and resolution times," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 283-303, June.
    7. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    utility maximisation; additional information; enlargement of filtrations; conditional measures; convex conjugate function; dual function; f-divergence;
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