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Backward Stochastic PDEs Related to the Utility Maximization Problem

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  • Michael Mania
  • Revaz Tevzadze

Abstract

We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an Rd-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial differential equation (BSPDE) related directly to the primal problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As examples the cases of power, exponential and logarithmic utilities are considered

Suggested Citation

  • Michael Mania & Revaz Tevzadze, 2008. "Backward Stochastic PDEs Related to the Utility Maximization Problem," ICER Working Papers - Applied Mathematics Series 07-2008, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:07-2008
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2008/ICERwp07-08.pdf
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    References listed on IDEAS

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    Cited by:

    1. Peter Imkeller & Anthony Réveillac & Jianing Zhang, 2011. "SOLVABILITY AND NUMERICAL SIMULATION OF BSDEs RELATED TO BSPDEs WITH APPLICATIONS TO UTILITY MAXIMIZATION," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 635-667.
    2. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CARF F-Series CARF-F-332, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Bernt Oksendal & Agnès Sulem, 2011. "Portfolio optimization under model uncertainty and BSDE games," Working Papers inria-00570532, HAL.
    4. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CIRJE F-Series CIRJE-F-891, CIRJE, Faculty of Economics, University of Tokyo.
    5. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," Papers 1306.3359, arXiv.org, revised Nov 2013.
    6. Claudia Ceci & Anna Gerardi, 2011. "Utility indifference valuation for jump risky assets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(2), pages 85-120, November.
    7. repec:dau:papers:123456789/7101 is not listed on IDEAS
    8. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," CARF F-Series CARF-F-321, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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    More about this item

    Keywords

    Backward stochastic partial di erential equation; utility maximization problem; semimartingale; incomplete markets;
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