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

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  • S\"oren Christensen
  • Marc Wittlinger
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://arxiv.org/

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    1. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    2. 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.
    3. 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.
    4. J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
    5. 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.
    6. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
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