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

Gerhold, S. ; Muhle-Karbe, J. ; Schachermayer, W.

In: Finance and Stochastics, 2013, vol. 17, no. 2, p. 325-354

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    Title
    • The dual optimizer for the growth-optimal portfolio under transaction costs
    Author
    • Gerhold, S.. Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Wien, Austria
    • Muhle-Karbe, J.. Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland
    • Schachermayer, W.. Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, 1090, Wien, Austria
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:314523
    Summary
    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