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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:

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    Keywords

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