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A note on Almgren-Chriss optimal execution problem with geometric Brownian motion

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  • Bastien Baldacci
  • Jerome Benveniste

Abstract

We solve explicitly the Almgren-Chriss optimal liquidation problem where the stock price process follows a geometric Brownian motion. Our technique is to work in terms of cash and to use functional analysis tools. We show that this framework extends readily to the case of a stochastic drift for the price process and the liquidation of a portfolio.

Suggested Citation

  • Bastien Baldacci & Jerome Benveniste, 2020. "A note on Almgren-Chriss optimal execution problem with geometric Brownian motion," Papers 2006.11426, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:2006.11426
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    File URL: http://arxiv.org/pdf/2006.11426
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    References listed on IDEAS

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    1. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    2. �lvaro Cartea & Sebastian Jaimungal, 2015. "Optimal execution with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1279-1291, August.
    3. Pierre Collin-Dufresne & Vyacheslav Fos, 2015. "Do Prices Reveal the Presence of Informed Trading?," Journal of Finance, American Finance Association, vol. 70(4), pages 1555-1582, August.
    4. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    5. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    6. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    7. Pierre Collin-Dufresne & Vyacheslav Fos, 2013. "Do Prices Reveal the Presence of Informed Trading?," Swiss Finance Institute Research Paper Series 13-69, Swiss Finance Institute, revised Sep 2015.
    8. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
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    Cited by:

    1. Bastien Baldacci & Jerome Benveniste & Gordon Ritter, 2021. "Optimal Turnover, Liquidity, and Autocorrelation," Papers 2110.03810, arXiv.org, revised Jan 2022.

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