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Comparative Statics of Trading Boundary in Finite Horizon Portfolio Selection with Proportional Transaction Costs

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  • Jintao Li
  • Shuaijie Qian

Abstract

We consider the Merton's problem with proportional transaction costs. It is well-known that the optimal investment strategy is characterized by two trading boundaries, i.e., the buy boundary and the sell boundary, between which is the no-trading region. We study how the two trading boundaries vary with transaction costs. We reveal that the cost-adjusted trading boundaries are monotone in transaction costs. Our result indicates that (i) the Merton line must lie between two cost-adjusted trading boundaries; (ii) when the Merton line is positive, the buy boundary and the sell boundary are monotone in transaction costs and the Merton line lies in the no-trading region as a result.

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  • Jintao Li & Shuaijie Qian, 2024. "Comparative Statics of Trading Boundary in Finite Horizon Portfolio Selection with Proportional Transaction Costs," Papers 2412.13669, arXiv.org.
    • Handle: RePEc:arx:papers:2412.13669
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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. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2019. "Optimal consumption and investment under transaction costs," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 483-506, April.
    3. 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.
    4. 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.
    5. Hong Liu & Mark Loewenstein, 2002. "Optimal Portfolio Selection with Transaction Costs and Finite Horizons," The Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 805-835.
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