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Asymptotic methods for transaction costs

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  • Eberhard Mayerhofer

Abstract

We propose a general approximation method for determining 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, 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 trading frequency and trade sizes to have satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity.

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  • Eberhard Mayerhofer, 2024. "Asymptotic methods for transaction costs," Papers 2407.07100, arXiv.org.
    • Handle: RePEc:arx:papers:2407.07100
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    References listed on IDEAS

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    1. 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.
    2. Eberhard Mayerhofer, 2024. "Almost Perfect Shadow Prices," Papers 2401.00970, arXiv.org, revised Feb 2024.
    3. Jan Kallsen & Johannes Muhle-Karbe, 2017. "The General Structure Of Optimal Investment And Consumption With Small Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 659-703, July.
    4. 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.
    5. Eberhard Mayerhofer, 2024. "Almost Perfect Shadow Prices," JRFM, MDPI, vol. 17(2), pages 1-18, February.
    6. Paolo Guasoni & Marko Hans Weber, 2020. "Nonlinear price impact and portfolio choice," Mathematical Finance, Wiley Blackwell, vol. 30(2), pages 341-376, April.
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