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Robust utility maximization for complete and incomplete market models

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  • Anne Gundel

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    Abstract

    We investigate the problem of maximizing the robust utility functional $\inf_{Q \in \mathcal{Q}} E_Qu(X)$ . We give the dual characterization for its solution for both a complete and an incomplete market model. To this end, we introduce the new notion of reverse f-projections and use techniques developed for f-divergences. This is a suitable tool to reduce the robust problem to the classical problem of utility maximization under a certain measure: the reverse f-projection. Furthermore, we give the dual characterization for a closely related problem, the minimization of expenditures given a minimum level of expected utility in a robust setting and for an incomplete market. Copyright Springer-Verlag Berlin/Heidelberg 2005

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 9 (2005)
    Issue (Month): 2 (04)
    Pages: 151-176

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    Handle: RePEc:spr:finsto:v:9:y:2005:i:2:p:151-176

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    Related research

    Keywords: f-divergences; utility maximization; robust utility functionals; model uncertainty; incomplete markets; duality;

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    Cited by:
    1. Alexander Schied, 2007. "Robust Optimal Control for a Consumption-investment Problem," SFB 649 Discussion Papers SFB649DP2007-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Xiaoxian Ma & Qingzhen Zhao & Jilin Qu, 2008. "Robust portfolio optimization with a generalized expected utility model under ambiguity," Annals of Finance, Springer, vol. 4(4), pages 431-444, October.
    3. Alexander Schied, 2008. "Robust optimal control for a consumption-investment problem," Computational Statistics, Springer, vol. 67(1), pages 1-20, February.
    4. Constantinos Kardaras & Scott Robertson, 2012. "Robust maximization of asymptotic growth," LSE Research Online Documents on Economics 44994, London School of Economics and Political Science, LSE Library.
    5. Wiebke Wittmüß, 2006. "Robust Optimization of Consumption with Random Endowment," SFB 649 Discussion Papers SFB649DP2006-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Gundel, Anne & Weber, Stefan, 2008. "Utility maximization under a shortfall risk constraint," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1126-1151, December.
    7. Grzegorz Hara\'nczyk & Wojciech S{\l}omczy\'nski & Tomasz Zastawniak, 2007. "Relative and Discrete Utility Maximising Entropy," Papers 0709.1281, arXiv.org.
    8. 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.
    9. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
    10. A. Hoseinzadeh & G. Mohtashami Borzadaran & G. Yari, 2012. "Aspects concerning entropy and utility," Theory and Decision, Springer, vol. 72(2), pages 273-285, February.
    11. Constantinos Kardaras & Scott Robertson, 2010. "Robust maximization of asymptotic growth," Papers 1005.3454, arXiv.org, revised Aug 2012.

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