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

2010/05/27 by Stefan Gerhold, Gerhold, Stefan, Johannes Muhle-Karbe +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #math.OC #math.PR #q-fin.PM

paper · pdf · doi:10.48550/arxiv.1005.5105

26 pages, 2 figures

arxiv created 2010/10/11 · arxiv updated 2010/10/12

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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• Discrete time shadow price revisited

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