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A Unified Approach to Portfolio Optimization with Linear Transaction Costs

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  • Valeri Zakamouline

    (Bodoe Graduate School of Business)

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    Abstract

    In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.

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    File URL: http://128.118.178.162/eps/ge/papers/0404/0404003.pdf
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    Bibliographic Info

    Paper provided by EconWPA in its series GE, Growth, Math methods with number 0404003.

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    Length: 36 pages
    Date of creation: 16 Apr 2004
    Date of revision: 21 Apr 2004
    Handle: RePEc:wpa:wuwpge:0404003

    Note: Type of Document - pdf; pages: 36
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    Web page: http://128.118.178.162

    Related research

    Keywords: portfolio choice; transaction costs; stochastic singular control; stochastic impulse control; computational methods;

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    1. Andriy Demchuk, 2002. "Portfolio Optimization with Concave Transaction Costs," FAME Research Paper Series rp103, International Center for Financial Asset Management and Engineering.
    2. Framstad, Nils Chr. & Oksendal, Bernt & Sulem, Agnes, 2001. "Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 233-257, April.
    3. Valeri Zakamouline, 2003. "American Option Pricing with Transaction Costs," Finance 0311012, EconWPA.
    4. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    5. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, 05.
    6. 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.
    7. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    8. A. E. Whalley & P. Wilmott, 1997. "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 307-324.
    9. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
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