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On utility maximization under convex portfolio constraints


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


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.

Suggested Citation

  • Kasper Larsen & Gordan v{Z}itkovi'c, 2011. "On utility maximization under convex portfolio constraints," Papers 1102.0346,, revised Feb 2013.
  • Handle: RePEc:arx:papers:1102.0346

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    References listed on IDEAS

    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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    Cited by:

    1. Kasper Larsen & Halil Mete Soner & Gordan v{Z}itkovi'c, 2017. "Conditional Davis Pricing," Papers 1702.02087,
    2. Takuji Arai, 2015. "Good deal bounds with convex constraints," Papers 1506.00396,
    3. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2015. "Non-Arbitrage Under Additional Information for Thin Semimartingale Models," Papers 1505.00997,
    4. Kasper Larsen & Halil Mete Soner & Gordan Žitković, 2016. "Facelifting in utility maximization," Finance and Stochastics, Springer, vol. 20(1), pages 99-121, January.
    5. Kasper Larsen & Halil Soner & Gordan Žitković, 2016. "Facelifting in utility maximization," Finance and Stochastics, Springer, vol. 20(1), pages 99-121, January.
    6. Takuji Arai, 2016. "Good deal bounds with convex constraints: --- examples and proofs ---," Keio-IES Discussion Paper Series 2016-017, Institute for Economics Studies, Keio University.
    7. repec:wsi:ijtafx:v:20:y:2017:i:02:n:s021902491750011x is not listed on IDEAS
    8. Pietro Siorpaes, 2015. "Optimal investment and price dependence in a semi-static market," Finance and Stochastics, Springer, vol. 19(1), pages 161-187, January.
    9. repec:bla:irvfin:v:17:y:2017:i:2:p:235-262 is not listed on IDEAS

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