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Relative entropy-regularized robust optimal order execution

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  • Meng Wang
  • Tai-Ho Wang

Abstract

The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent's goal is to maximize an objective functional associated with his profit-and-loss of trading and simultaneously minimize the execution risk and the market's liquidity and uncertainty. We model the market's liquidity and uncertainty by the principle of least relative entropy associated with the market volume. The problem of order execution is made into a relative entropy-regularized stochastic differential game. Standard argument of dynamic programming yields that the value function of the differential game satisfies a relative entropy-regularized Hamilton-Jacobi-Isaacs (rHJI) equation. Under the assumptions of linear-quadratic model with Gaussian prior, the rHJI equation reduces to a system of Riccati and linear differential equations. Further imposing constancy of the corresponding coefficients, the system of differential equations can be solved in closed form, resulting in analytical expressions for optimal strategy and trajectory as well as the posterior distribution of market volume. Numerical examples illustrating the optimal strategies and the comparisons with conventional trading strategies are conducted.

Suggested Citation

  • Meng Wang & Tai-Ho Wang, 2023. "Relative entropy-regularized robust optimal order execution," Papers 2311.06476, arXiv.org, revised Sep 2024.
  • Handle: RePEc:arx:papers:2311.06476
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    References listed on IDEAS

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    1. 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.
    2. Francesca Mariani & Lorella Fatone, 2022. "Optimal solution of the liquidation problem under execution and price impact risks," Quantitative Finance, Taylor & Francis Journals, vol. 22(6), pages 1037-1049, June.
    3. Xue Cheng & Marina Di Giacinto & Tai-Ho Wang, 2019. "Optimal execution with dynamic risk adjustment," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1662-1677, October.
    4. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    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. René Carmona & Kevin Webster, 2019. "The self-financing equation in limit order book markets," Finance and Stochastics, Springer, vol. 23(3), pages 729-759, July.
    7. 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.
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