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

S. Gerhold (), J. Muhle-Karbe () and W. Schachermayer ()

Finance and Stochastics, 2013, vol. 17, issue 2, 325-354

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. Copyright Springer-Verlag 2013

Keywords: Transaction costs; Growth-optimal portfolio; Shadow price; 91B28; 91B16; 60H10; G11 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (20)

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DOI: 10.1007/s00780-011-0165-9

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