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On an investment-consumption model with transaction costs: an asymptotic analysis

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  • C. Atkinson
  • B. Al-Ali

Abstract

In this paper we examine the Akian, Menaldi and Sulem (1996) model for the optimal management of a portfolio, when there are transaction costs which are equal to a fixed percentage of the amount transacted. We analyse this model in the realistic limit of small transaction costs. 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 & B. Al-Ali, 1997. "On an investment-consumption model with transaction costs: an asymptotic analysis," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(2), pages 109-133.
    • Handle: RePEc:taf:apmtfi:v:4:y:1997:i:2:p:109-133
    DOI: 10.1080/13504869700000003
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    References listed on IDEAS

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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    Cited by:

    1. 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.

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