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Growth-optimal portfolios under transaction costs

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  • Jan Palczewski
  • Lukasz Stettner

Abstract

This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that there exists a self-financing trading strategy maximizing the average growth rate of the portfolio wealth. We show that this strategy has a Markovian form. Our result is obtained by large deviations estimates on empirical measures of the price process and by a generalization of the vanishing discount method to discontinuous transition operators.

Suggested Citation

  • Jan Palczewski & Lukasz Stettner, 2007. "Growth-optimal portfolios under transaction costs," Papers 0707.3198, arXiv.org.
    • Handle: RePEc:arx:papers:0707.3198
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    References listed on IDEAS

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    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
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    3. Marianne Akian & Agnès Sulem & Michael I. Taksar, 2001. "Dynamic Optimization of Long‐Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 153-188, April.
    4. Garud Iyengar, 2005. "Universal Investment In Markets With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 359-371, April.
    5. W. H. Fleming & S. J. Sheu, 2000. "Risk‐Sensitive Control and an Optimal Investment Model," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 197-213, April.
    6. Aase, Knut K. & Øksendal, Bernt, 1988. "Admissible investment strategies in continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 291-301, December.
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