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Balancing small fixed and proportional transaction cost in trading strategies

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  • Jose V. Alcala
  • Arash Fahim

Abstract

Transaction costs appear in financial markets in more than one form. There are several results in the literature on small proportional transaction cost and not that many on fixed transaction cost. In the present work, we heuristically study the effect of both types of transaction cost by focusing on a portfolio optimization. Here we assume the presence of fixed transaction cost and that there is a balance between fixed and proportional transaction cost, such that none of them dominates the other, asymptotically. We find out that the deviation of value function, when the fixed transaction cost is $\varepsilon$, from the Merton value function, without transaction cost, is of order $\varepsilon^1/2$ which is different from the pure proportional cost of $\varepsilon^2/3$. Based on this, we propose an expansion for the value function in terms of powers of $\varepsilon^1/2$.

Suggested Citation

  • Jose V. Alcala & Arash Fahim, 2013. "Balancing small fixed and proportional transaction cost in trading strategies," Papers 1304.7562, arXiv.org.
    • Handle: RePEc:arx:papers:1304.7562
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    References listed on IDEAS

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    1. 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, May.
    2. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
    3. Halil Mete Soner & Nizar Touzi, 2012. "Homogenization and Asymptotics for Small Transaction Costs," Swiss Finance Institute Research Paper Series 12-13, Swiss Finance Institute.
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    Cited by:

    1. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
    2. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.

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