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Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty

Author

Listed:
  • Brian Bulthuis

    (Two Sigma Investments, New York, NY 10006, USA)

  • Julio Concha

    (Two Sigma Investments, New York, NY 10006, USA)

  • Tim Leung

    (#x2020;Applied Mathematics Department, University of Washington, Seattle WA 98195, USA)

  • Brian Ward

    (#x2021;Industrial Engineering & Operations Research (IEOR) Department, Columbia University, New York, NY 10027, USA)

Abstract

We study the optimal execution of market and limit orders with permanent and temporary price impacts as well as uncertainty in the filling of limit orders. Our continuous-time model incorporates a trade speed limiter and a trade director to provide better control on the trading rates. We formulate a stochastic control problem to determine the optimal dynamic strategy for trade execution, with a quadratic terminal penalty to ensure complete liquidation. In addition, we identify conditions on the model parameters to ensure optimality of the controls and finiteness of the associated value functions. For comparison, we also solve the schedule-following optimal execution problem that penalizes deviations from an order schedule. Numerical results are provided to illustrate the optimal market and limit orders over time.

Suggested Citation

  • Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2017. "Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:02n03:n:s2424786317500207
    DOI: 10.1142/S2424786317500207
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    References listed on IDEAS

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    1. Charles-Albert Lehalle & Sophie Laruelle (ed.), 2013. "Market Microstructure in Practice," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8967, September.
    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. Fabien Guilbaud & Huyên Pham, 2013. "Optimal high-frequency trading with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 79-94, January.
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    7. Xue Cheng & Marina Di Giacinto & Tai-Ho Wang, 2017. "Optimal execution with uncertain order fills in Almgren–Chriss framework," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 55-69, January.
    8. Kiseop Lee, 2008. "Risk minimization under budget constraints," Journal of Risk Finance, Emerald Group Publishing, vol. 9(1), pages 71-80, January.
    9. Peter Kratz & Torsten Schöneborn, 2015. "Portfolio Liquidation In Dark Pools In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 496-544, July.
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    Cited by:

    1. Luca Lalor & Anatoliy Swishchuk, 2024. "Market Simulation under Adverse Selection," Papers 2409.12721, arXiv.org, revised Mar 2025.
    2. Xue Cheng & Marina Di Giacinto & Tai-Ho Wang, 2019. "Optimal execution with dynamic risk adjustment," Papers 1901.00617, arXiv.org, revised Jul 2019.
    3. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    4. Chuheng Zhang & Yitong Duan & Xiaoyu Chen & Jianyu Chen & Jian Li & Li Zhao, 2023. "Towards Generalizable Reinforcement Learning for Trade Execution," Papers 2307.11685, arXiv.org.

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