The dual optimizer for the growth-optimal portfolio under transaction costs
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1005.5105.
Date of creation: May 2010
Date of revision: Oct 2010
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-04 (All new papers)
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