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Optimal position-building strategies in competition

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  • Neil A. Chriss

Abstract

This paper develops a mathematical framework for building a position in a stock over a fixed period of time while in competition with one or more other traders doing the same thing. We develop a game-theoretic framework that takes place in the space of trading strategies where action sets are trading strategies and traders try to devise best-response strategies to their adversaries. In this setup trading is guided by a desire to minimize the total cost of trading arising from a mixture of temporary and permanent market impact caused by the aggregate level of trading including the trader and the competition. We describe a notion of equilibrium strategies, show that they exist and provide closed-form solutions.

Suggested Citation

  • Neil A. Chriss, 2024. "Optimal position-building strategies in competition," Papers 2409.03586, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2409.03586
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    References listed on IDEAS

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    1. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    2. Hautsch, Nikolaus & Huang, Ruihong, 2012. "The market impact of a limit order," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 501-522.
    3. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    4. 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.
    5. Ryan Donnelly, 2022. "Optimal Execution: A Review," Applied Mathematical Finance, Taylor & Francis Journals, vol. 29(3), pages 181-212, May.
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