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Long Time Growth Optimal Portfolio with Transaction Costs

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Optimality and Risk - Modern Trends in Mathematical Finance

Abstract

Discrete and continuous growth optimal portfolio optimization over long time horizon is studied. Proportional transaction costs consisting of fixed proportional plus proportional to the volume of transaction are considered. An obligatory diversification is imposed, which allows the process of portions of capital invested in assets to be ergodic. Existence of solutions to suitable Bellman equations is proved and the form of optimal strategies is shown. For continuous time model an additional fixed deterministic delay in transactions is assumed.

Research supported by MNiSzW grant P03A 01328.

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References

  1. Akian, M., Sulem, A., Taksar, M.I.: Dynamic optimization of a long-term growth rate for a portfolio with transaction costs and logaritmic utility. Math. Financ. 5, 153–188 (2001)

    Article  MathSciNet  Google Scholar 

  2. Algoet, P.H., Cover, T.M.: Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. Ann. Probab. 16, 876–898 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  3. Applebaum, D.: Lévy Processes and Stochastic Calculus. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  4. Blumenthal, R.M., Getoor, R.K.: Markov Processes and Potential Theory. Academic Press, San Diego (1968)

    MATH  Google Scholar 

  5. Doob, J.L.: Stochastic Processes. Chapman & Hall, London (1953)

    MATH  Google Scholar 

  6. Györfi, L., Vajda, I.: Growth optimal portfolio selection strategies with proportional transaction costs. Preprint (2007)

    Google Scholar 

  7. Irle, A., Sass, J.: Good portfolio strategies under transaction costs: a renewal theoretic approach. In: Grossinho, M.R., Shiryaev, A.N., Esquivel, M., Oliveira, P.E. (eds.) Stochastic Finance, pp. 321–341. Springer, Berlin (2006)

    Chapter  Google Scholar 

  8. Iyengar, G.: Universal investment in markets with transaction costs. Math. Financ. 15, 359–371

    Google Scholar 

  9. Kabanov, Y., Klüppelberg, C.: A geometric approach to portfolio optimization in models with transaction costs. Finance Stoch. 8, 207–227 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kelly, J.L.: A new interpretation of information rate. Bell Syst. Tech. J. 35, 917–926 (1956)

    Google Scholar 

  11. Korn, R.: Portfolio optimisation with strictly positive transaction costs and impulse control. Finance Stoch. 2, 85–114 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Magill, M.J., Constantanides, M.: Portfolio selection with transaction costs. J. Econ. Theory 13, 245–263 (1976)

    Article  MATH  Google Scholar 

  13. Morton, A.J., Pliska, S.R.: Optimal portfolio management with fixed transaction costs. Math. Financ. 5, 337–356 (1995)

    Article  MATH  Google Scholar 

  14. Palczewski, J., Stettner, L.: Maximization of the portfolio growth rate under fixed and proportional transaction costs. Commun. Inf. Syst. 7, 31–58 (2007)

    MATH  MathSciNet  Google Scholar 

  15. Palczewski, J., Stettner, L.: Growth-optimal portfolios under transaction costs. Appl. Math. 35, 1–31 (2008)

    MATH  MathSciNet  Google Scholar 

  16. Royden, H.L.: Real Analysis. Macmillan, New York (1968)

    Google Scholar 

  17. Schäfer, D.: Nonparametric Estimation for Financial Investment under Log-Utility. PhD Dissertation, Mathematical Institute University of Stuttgart, Aachen (2002)

    Google Scholar 

  18. Scheffe, H.: A useful convergence theorem for probability distributions. Ann. Math. Stat. 18, 434–438 (1947)

    Article  MATH  MathSciNet  Google Scholar 

  19. Stettner, L.: Discrete time risk sensitive portfolio optimization with consumption and proportional transaction costs. Appl. Math. 32(4), 395–404 (2005)

    MATH  MathSciNet  Google Scholar 

  20. Stettner, L.: Discrete time infinite horizon risk sensitive portfolio selection with proportional transaction costs. In: Stettner, L. (ed.) Advances in Mathematics of Finance. Banach Center Publications, vol. 86, pp. 231–241. PWN, Warsaw (2008).

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-956, Warsaw, Poland

    Lukasz Stettner

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  1. Lukasz Stettner
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Stettner, L. (2009). Long Time Growth Optimal Portfolio with Transaction Costs. In: Optimality and Risk - Modern Trends in Mathematical Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02608-9_13

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