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Optimal Portfolio Management With Fixed Transaction Costs

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  • Andrew J. Morton
  • Stanley R. Pliska
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    Abstract

    We study optimal portfolio management policies for an investor who must pay a transaction cost equal to a fixed Traction of his portfolio value each time he trades. We focus on the infinite horizon objective function of maximizing the asymptotic growth rate, so me optimal policies we derive approximate those of an investor with logarithmic utility at a distant horizon. When investment opportunities are modeled as "m" correlated geometric Brownian motion stocks and a riskless bond, we show that the optimal policy reduces to solving a single stopping time problem. When there is a single risky stock, we give a system of equations whose solution determines the optima! rule. We use numerical methods to solve for the optima! policy when there are two risky stocks. We study several specific examples and observe the general qualitative result that, even with very low transaction cost levels, the optimal policy entails very infrequent trading. Copyright 1995 Blackwell Publishers.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 5 (1995)
    Issue (Month): 4 ()
    Pages: 337-356

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    Handle: RePEc:bla:mathfi:v:5:y:1995:i:4:p:337-356

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    Cited by:
    1. Elyès Jouini & Hédi Kallal & Clotilde Napp, 1999. "Arbitrage and Viability in Securities Markets with Fixed Trading Costs," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-033, New York University, Leonard N. Stern School of Business-.
    2. He, Hua & Mamaysky, Harry, 2005. "Dynamic trading policies with price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 891-930, May.
    3. Siu Lung Law & Chiu Fan Lee & Sam Howison & Jeff N. Dewynne, 2007. "Correlated multi-asset portfolio optimisation with transaction cost," Papers 0705.1949, arXiv.org, revised May 2009.
    4. Zhang, Wei-Guo & Xiao, Wei-Lin & Xu, Wei-Jun, 2010. "A possibilistic portfolio adjusting model with new added assets," Economic Modelling, Elsevier, vol. 27(1), pages 208-213, January.
    5. Edison G. Yu, 2013. "Dynamic market participation and endogenous information aggregation," Working Papers 13-42, Federal Reserve Bank of Philadelphia.
    6. Xi-li Zhang & Wei-Guo Zhang & Wei-jun Xu & Wei-Lin Xiao, 2010. "Possibilistic Approaches to Portfolio Selection Problem with General Transaction Costs and a CLPSO Algorithm," Computational Economics, Society for Computational Economics, vol. 36(3), pages 191-200, October.
    7. Gautam Goswami & Milind Shrikhande & Liuren Wu, 2002. "A Dynamic Equilibrium Model of Real Exchange Rates with General Transaction Costs," Finance 0207016, EconWPA.
    8. Gupta, Pankaj & Mittal, Garima & Mehlawat, Mukesh Kumar, 2013. "Expected value multiobjective portfolio rebalancing model with fuzzy parameters," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 190-203.
    9. Claas Prelle & Albrecht Irle, 2008. "A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets," Kiel Working Papers 1449, Kiel Institute for the World Economy.
    10. 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.
    11. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    12. Muthuraman, Kumar, 2007. "A computational scheme for optimal investment - consumption with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1132-1159, April.

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