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Shadow price in the power utility case

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  • Attila Herczegh
  • Vilmos Prokaj

Abstract

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.

Suggested Citation

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

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
    3. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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    Cited by:

    1. Paolo Guasoni & Johannes Muhle-Karbe, 2012. "Portfolio Choice with Transaction Costs: a User's Guide," Papers 1207.7330, arXiv.org.
    2. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "A multi-asset investment and consumption problem with transaction costs," Papers 1612.01327, arXiv.org.
    3. Johannes Muhle-Karbe & Ren Liu, 2012. "Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints," Papers 1205.4588, arXiv.org, revised Jan 2013.
    4. Yiqing Lin & Junjian Yang, 2016. "Utility maximization problem with random endowment and transaction costs: when wealth may become negative," Papers 1604.08224, arXiv.org, revised Sep 2016.
    5. Jin Hyuk Choi, 2016. "Optimal consumption and investment with liquid and illiquid assets," Papers 1602.06998, arXiv.org, revised Jan 2019.
    6. Lingqi Gu & Yiqing Lin & Junjian Yang, 2016. "On the existence of shadow prices for optimal investment with random endowment," Papers 1602.01109, arXiv.org, revised Feb 2017.
    7. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "Optimal consumption and investment under transaction costs," Papers 1612.00720, arXiv.org.
    8. 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.
    9. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2019. "A multi-asset investment and consumption problem with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 641-676, July.
    10. Christoph Belak & Jörn Sass, 2019. "Finite-horizon optimal investment with transaction costs: construction of the optimal strategies," Finance and Stochastics, Springer, vol. 23(4), pages 861-888, October.

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