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Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs

  • S\"oren Christensen
  • Marc Wittlinger
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    In this paper we investigate a new class of growth rate maximization problems based on impulse control strategies such that the average number of trades per time unit does not exceed a fixed level. Moreover, we include proportional transaction costs to make the portfolio problem more realistic. We provide a Verification Theorem to compute the optimal growth rate as well as an optimal trading strategy. Furthermore, we prove the existence of a constant boundary strategy which is optimal. At the end, we compare our approach to other discrete-time growth rate maximization problems in numerical examples. It turns out that constant boundary strategies with a small average number of trades per unit perform nearly as good as the classical optimal solutions with infinite activity.

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    File URL: http://arxiv.org/pdf/1209.0305
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    Paper provided by arXiv.org in its series Papers with number 1209.0305.

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    Date of creation: Sep 2012
    Date of revision: Jun 2013
    Handle: RePEc:arx:papers:1209.0305
    Contact details of provider: Web page: http://arxiv.org/

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    1. J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
    2. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    3. Huy�n Pham & Peter Tankov, 2008. "A Model Of Optimal Consumption Under Liquidity Risk With Random Trading Times," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 613-627.
    4. Yuri Kabanov & Claudia Klüppelberg, 2004. "A geometric approach to portfolio optimization in models with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 207-227, 05.
    5. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    6. Koichi Matsumoto, 2006. "Optimal portfolio of low liquid assets with a log-utility function," Finance and Stochastics, Springer, vol. 10(1), pages 121-145, 01.
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