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On utility maximization under convex portfolio constraints

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  • Kasper Larsen
  • Gordan \v{Z}itkovi\'c
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    Abstract

    We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin; that is, it may be inadmissible for an investor to hold no risky investment at all. Such a setup subsumes the classical constrained utility-maximization problem, as well as the problem where illiquid assets or a random endowment are present. Our main result establishes the existence of optimal trading strategies in such models under no smoothness requirements on the utility function. The result also shows that, up to attainment, the dual optimization problem can be posed over a set of countably-additive probability measures, thus eschewing the need for the usual finitely-additive enlargement.

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    File URL: http://arxiv.org/pdf/1102.0346
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1102.0346.

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    Date of creation: Feb 2011
    Date of revision: Feb 2013
    Publication status: Published in Annals of Applied Probability 2013, Vol. 23, No. 2, 665-692
    Handle: RePEc:arx:papers:1102.0346

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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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