Growth-optimal portfolios under transaction costs

Volume 35 / 2008

Jan Palczewski, /Lukasz Stettner Applicationes Mathematicae 35 (2008), 1-31 MSC: Primary 91B28; Secondary 93E20. DOI: 10.4064/am35-1-1


This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depends 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.


  • Jan PalczewskiSchool of Mathematics
    University of Leeds
    Leeds LS2 9JT, UK
    Faculty of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
  • /Lukasz StettnerInstitute of Mathematics
    Polish Academy of Sciences
    /Sniadeckich 8
    00-956 Warszawa, Poland

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