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Multi-asset portfolio selection problem with transaction costs

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  • Akian, Marianne
  • Menaldi, Jose Luis
  • Sulem, Agnès

Abstract

This paper considers the optimal consumption and investiment policy for an investor who has available one bank account paying a fixed interest rate r and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption. Dynamic Programming leads to a Variational Inequality for the value function which is solved by using a numerical algorithm based on policies iterations and multigrid methods. Numerical results are displayed for n = 1 and n = 2.

Suggested Citation

  • Akian, Marianne & Menaldi, Jose Luis & Sulem, Agnès, 1995. "Multi-asset portfolio selection problem with transaction costs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 163-172.
    • Handle: RePEc:eee:matcom:v:38:y:1995:i:1:p:163-172
    DOI: 10.1016/0378-4754(93)E0079-K
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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.
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    3. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    4. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
    7. S. E. Shreve & H. M. Soner & G.‐L. Xu, 1991. "Optimal Investment and Consumption With Two Bonds and Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 53-84, July.
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    Cited by:

    1. David Hobson & Yeqi Zhu, 2014. "Multi-asset consumption-investment problems with infinite transaction costs," Papers 1409.8037, arXiv.org.
    2. Stanley Pliska & Kiyoshi Suzuki, 2004. "Optimal tracking for asset allocation with fixed and proportional transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 233-243.
    3. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2019. "A multi-asset investment and consumption problem with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 641-676, July.
    4. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "A multi-asset investment and consumption problem with transaction costs," Papers 1612.01327, arXiv.org.

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