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

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Abstract

We consider the maximization of the long-term growth rate in the Black–Scholes model under proportional transaction costs as in Taksar et al. (Math. Oper. Res. 13:277–294, 1988). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341–1358, 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 one 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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Authors and Affiliations

  1. Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Wien, Austria

    S. Gerhold

  2. Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland

    J. Muhle-Karbe

  3. Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, 1090, Wien, Austria

    W. Schachermayer

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  1. S. Gerhold
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  2. J. Muhle-Karbe
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  3. W. Schachermayer
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Correspondence to J. Muhle-Karbe.

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Gerhold, S., Muhle-Karbe, J. & Schachermayer, W. The dual optimizer for the growth-optimal portfolio under transaction costs. Finance Stoch 17, 325–354 (2013). https://doi.org/10.1007/s00780-011-0165-9

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  • DOI: https://doi.org/10.1007/s00780-011-0165-9

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