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

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  • Stefan Gerhold
  • Johannes Muhle-Karbe
  • Walter Schachermayer

Abstract

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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  • Stefan Gerhold & Johannes Muhle-Karbe & Walter Schachermayer, 2010. "The dual optimizer for the growth-optimal portfolio under transaction costs," Papers 1005.5105, arXiv.org, revised Oct 2010.
    • Handle: RePEc:arx:papers:1005.5105
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    References listed on IDEAS

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    6. J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
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    Cited by:

    1. Paolo Guasoni & Johannes Muhle-Karbe, 2011. "Long Horizons, High Risk Aversion, and Endogeneous Spreads," Papers 1110.1214, arXiv.org, revised Jul 2012.

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