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The dual optimizer for the growth-optimal portfolio under transaction costs

  • Stefan Gerhold
  • Johannes Muhle-Karbe
  • Walter Schachermayer
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    We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar, Klass and Assaf [Math. Oper. Res. 13, 1988]. Similarly as in Kallsen and Muhle-Karbe [Ann. Appl. Probab., 20, 2010] for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rate.

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    File URL: http://arxiv.org/pdf/1005.5105
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    Paper provided by arXiv.org in its series Papers with number 1005.5105.

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    Date of creation: May 2010
    Date of revision: Oct 2010
    Handle: RePEc:arx:papers:1005.5105
    Contact details of provider: Web page: http://arxiv.org/

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    1. Hong Liu & Mark Loewenstein, 2002. "Optimal Portfolio Selection with Transaction Costs and Finite Horizons," Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 805-835.
    2. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-95, June.
    3. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165.
    4. A. E. Whalley & P. Wilmott, 1997. "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 307-324.
    5. J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
    6. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, 05.
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