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Optimal execution with uncertain order fills in Almgren–Chriss framework

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  • Xue Cheng
  • Marina Di Giacinto
  • Tai-Ho Wang

Abstract

The classical price impact model of Almgren and Chriss is extended to incorporate the uncertainty of order fills. The extended model can be recast as alternatives to uncertain impact models and stochastic liquidity models. Optimal strategies are determined by maximizing the expected final profit and loss (P&L) and various P&L-risk tradeoffs including utility maximization. Closed form expressions for optimal strategies are obtained in linear cases. The results suggest a type of adaptive volume weighted average price, adaptive percentage of volume and adaptive Almgren–Chriss strategies. VWAP and classical Almgren–Chriss strategies are recovered as limiting cases with a different characteristic time scale of liquidation for the latter.

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  • 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.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:1:p:55-69
    DOI: 10.1080/14697688.2016.1185531
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    Cited by:

    1. Meng Wang & Tai-Ho Wang, 2023. "Relative entropy-regularized robust optimal order execution," Papers 2311.06476, arXiv.org, revised Sep 2024.
    2. 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.
    3. Marina Di Giacinto & Claudio Tebaldi & Tai-Ho Wang, 2021. "Optimal order execution under price impact: A hybrid model," Papers 2112.02228, arXiv.org, revised Aug 2022.
    4. Qixuan Luo & Shijia Song & Handong Li, 2023. "Research on the Effects of Liquidation Strategies in the Multi-asset Artificial Market," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1721-1750, December.
    5. Xue Cheng & Marina Di Giacinto & Tai-Ho Wang, 2019. "Optimal execution with dynamic risk adjustment," Papers 1901.00617, arXiv.org, revised Jul 2019.
    6. Julien Vaes & Raphael Hauser, 2018. "Optimal Trade Execution with Uncertain Volume Target," Papers 1810.11454, arXiv.org, revised Sep 2021.

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