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Utility duality under additional information: conditional measures versus filtration enlargements

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  • Stefan Ankirchner

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.

Suggested Citation

  • Stefan Ankirchner, 2005. "Utility duality under additional information: conditional measures versus filtration enlargements," SFB 649 Discussion Papers SFB649DP2005-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2005-029
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    References listed on IDEAS

    as
    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. Stefan Ankirchner & Steffen Dereich & Peter Imkeller, 2005. "The Shannon Information of Filtrations and the Additional Logarithmic Utility of Insiders," SFB 649 Discussion Papers SFB649DP2005-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
    4. 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.
    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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    More about this item

    Keywords

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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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