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Asymptotic Methods for Transaction Costs

Author

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  • Eberhard Mayerhofer

    (Department of Mathematics & Statistics, University of Limerick, V94 T9PX Limerick, Ireland)

Abstract

We propose a general approximation method for the determination of optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems, from optimally tracking benchmarks and hedging the log contract to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between the trading frequency and trade size to ensure satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity.

Suggested Citation

  • Eberhard Mayerhofer, 2024. "Asymptotic Methods for Transaction Costs," Risks, MDPI, vol. 12(4), pages 1-32, April.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:4:p:64-:d:1369971
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    References listed on IDEAS

    as
    1. S. Gerhold & J. Muhle-Karbe & W. Schachermayer, 2013. "The dual optimizer for the growth-optimal portfolio under transaction costs," Finance and Stochastics, Springer, vol. 17(2), pages 325-354, April.
    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.
    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. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
    Full references (including those not matched with items on IDEAS)

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