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Shadow price in the power utility case

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  • Attila Herczegh
  • Vilmos Prokaj
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    Abstract

    We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner (1994). Similarly to Kallsen and Muhle-Karbe (2010), 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. In doing so we explore and exploit the strong relationship between the shadow price and the Hamilton-Jacobi-Bellman-equation.

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    File URL: http://arxiv.org/pdf/1112.4385
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1112.4385.

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    Date of creation: Dec 2011
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    Handle: RePEc:arx:papers:1112.4385

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    Web page: http://arxiv.org/

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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. Johannes Muhle-Karbe & Ren Liu, 2012. "Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints," Papers 1205.4588, arXiv.org, revised Jan 2013.
    3. Paolo Guasoni & Johannes Muhle-Karbe, 2012. "Portfolio Choice with Transaction Costs: a User's Guide," Papers 1207.7330, arXiv.org.

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