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Utility maximization in incomplete markets

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  • Ying Hu
  • Peter Imkeller
  • Matthias Muller
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    Abstract

    We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under these constraints are identified as stochastic processes which usually are supermartingales, and even martingales for particular strategies. These strategies are seen to be optimal, and the corresponding value functions determined simply by the initial values of the supermartingales. We separately treat the cases of exponential, power and logarithmic utility.

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    File URL: http://arxiv.org/pdf/math/0508448
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number math/0508448.

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    Date of creation: Aug 2005
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    Publication status: Published in Annals of Applied Probability 2005, Vol. 15, No. 3, 1691-1712
    Handle: RePEc:arx:papers:math/0508448

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    Web page: http://arxiv.org/

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    1. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
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