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Optimal Execution under Liquidity Uncertainty

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Listed:
  • Etienne Chevalier
  • Yadh Hafsi
  • Vathana Ly Vath
  • Sergio Pulido

Abstract

We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. This resilience is modeled through a potentially arbitrary limit-order book shape. To account for liquidity dynamics, we introduce a stochastic volume effect governing the recovery of the deviation process, which represents the difference between the impacted and unaffected price. Additionally, we incorporate stochastic liquidity variations through a regime-switching Markov chain to capture abrupt shifts in market conditions. We study this singular control problem, where the trader optimally determines the timing and rate of purchases to minimize execution costs. The associated value function to this optimization problem is shown to satisfy a system of variational Hamilton-Jacobi-Bellman inequalities. Moreover, we establish that it is the unique viscosity solution to this HJB system and study the analytical properties of the free boundary separating the execution and continuation regions. To illustrate our results, we present numerical examples under different limit-order book configurations, highlighting the interplay between price impact, resilience dynamics, and stochastic liquidity regimes in shaping the optimal execution strategy.

Suggested Citation

  • Etienne Chevalier & Yadh Hafsi & Vathana Ly Vath & Sergio Pulido, 2025. "Optimal Execution under Liquidity Uncertainty," Papers 2506.11813, arXiv.org.
    • Handle: RePEc:arx:papers:2506.11813
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    References listed on IDEAS

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    1. Felix Dammann & Giorgio Ferrari, 2023. "Optimal execution with multiplicative price impact and incomplete information on the return," Finance and Stochastics, Springer, vol. 27(3), pages 713-768, July.
    2. Antje Fruth & Torsten Schöneborn & Mikhail Urusov, 2019. "Optimal trade execution in order books with stochastic liquidity," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 507-541, April.
    3. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Tóth, 2018. "Linear models for the impact of order flow on prices. I. History dependent impact models," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 903-915, June.
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