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Shadow price in the power utility case


  • Attila Herczegh
  • Vilmos Prokaj


We consider the problem of maximizing expected power utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in Shreve and Soner [Ann. Appl. Probab. 4 (1994) 609-692]. Similar to Kallsen and Muhle-Karbe [Ann. Appl. Probab. 20 (2010) 1341-1358], we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy.

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  • Attila Herczegh & Vilmos Prokaj, 2011. "Shadow price in the power utility case," Papers 1112.4385,, revised Sep 2015.
  • Handle: RePEc:arx:papers:1112.4385

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    Cited by:

    1. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2013. "On the existence of shadow prices," Finance and Stochastics, Springer, vol. 17(4), pages 801-818, October.
    2. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "A multi-asset investment and consumption problem with transaction costs," Papers 1612.01327,
    3. Johannes Muhle-Karbe & Ren Liu, 2012. "Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints," Papers 1205.4588,, revised Jan 2013.
    4. Paolo Guasoni & Johannes Muhle-Karbe, 2012. "Portfolio Choice with Transaction Costs: a User's Guide," Papers 1207.7330,
    5. Yiqing Lin & Junjian Yang, 2016. "Utility maximization problem with random endowment and transaction costs: when wealth may become negative," Papers 1604.08224,, revised Sep 2016.
    6. Jin Hyuk Choi, 2016. "Optimal investment and consumption with liquid and illiquid assets," Papers 1602.06998,, revised Jan 2018.
    7. Lingqi Gu & Yiqing Lin & Junjian Yang, 2016. "On the existence of shadow prices for optimal investment with random endowment," Papers 1602.01109,, revised Feb 2017.
    8. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "Optimal consumption and investment under transaction costs," Papers 1612.00720,

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