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Portfolio Management With Transaction Costs: An Asymptotic Analysis Of The Morton And Pliska Model


  • C. Atkinson
  • P. Wilmott


We examine the Morton and Pliska (1993) model for the optimal management of a portfolio when there are transaction costs proportional to a fixed fraction of the portfolio value. We analyze this model in the realistic case of small transaction costs by conducting a perturbation analysis about the no‐transaction‐cost solution. Although the full problem is a free‐boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.

Suggested Citation

  • C. Atkinson & P. Wilmott, 1995. "Portfolio Management With Transaction Costs: An Asymptotic Analysis Of The Morton And Pliska Model," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 357-367, October.
  • Handle: RePEc:bla:mathfi:v:5:y:1995:i:4:p:357-367
    DOI: 10.1111/j.1467-9965.1995.tb00072.x

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    1. repec:spr:compst:v:62:y:2005:i:2:p:319-343 is not listed on IDEAS
    2. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2004. "Asset Prices and Trading Volume under Fixed Transactions Costs," Journal of Political Economy, University of Chicago Press, vol. 112(5), pages 1054-1090, October.
    3. Cohen, Samuel N. & Henckel, Timo & Menzies, Gordon D. & Muhle-Karbe, Johannes & Zizzo, Daniel J., 2019. "Switching cost models as hypothesis tests," Economics Letters, Elsevier, vol. 175(C), pages 32-35.
    4. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302,, revised May 2017.
    5. Nabeel Butt, 2019. "On Discrete Probability Approximations for Transaction Cost Problems," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 365-389, September.
    6. Gautam Goswami & Milind Shrikhande & Liuren Wu, 2002. "A Dynamic Equilibrium Model of Real Exchange Rates with General Transaction Costs," Finance 0207016, University Library of Munich, Germany.
    7. Valeri Zakamouline, 2005. "A unified approach to portfolio optimization with linear transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 319-343, November.
    8. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    9. Kogan, Leonid, 2001. "An equilibrium model of irreversible investment," Journal of Financial Economics, Elsevier, vol. 62(2), pages 201-245, November.
    10. Andriy Demchuk, 2002. "Portfolio Optimization with Concave Transaction Costs," FAME Research Paper Series rp103, International Center for Financial Asset Management and Engineering.
    11. Liu, Cong & Zheng, Harry, 2016. "Asymptotic analysis for target asset portfolio allocation with small transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 59-68.
    12. Valeri Zakamouline, 2004. "A Unified Approach to Portfolio Optimization with Linear Transaction Costs," GE, Growth, Math methods 0404003, University Library of Munich, Germany, revised 28 Apr 2004.
    13. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958,
    14. Graziella Pacelli & Maria Cristina Recchioni & Francesco Zirilli, 1999. "A hybrid method for pricing European options based on multiple assets with transaction costs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 61-85.
    15. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802,, revised Oct 2013.
    16. Krastyu Georgiev & Young Kim & Stoyan Stoyanov, 2015. "Periodic portfolio revision with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 337-359, June.
    17. Yaroslav Melnyk & Frank Thomas Seifried, 2018. "Small†cost asymptotics for long†term growth rates in incomplete markets," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 668-711, April.
    18. Siu Lung Law & Chiu Fan Lee & Sam Howison & Jeff N. Dewynne, 2007. "Correlated multi-asset portfolio optimisation with transaction cost," Papers 0705.1949,, revised May 2009.
    19. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833,, revised Jul 2017.

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