Optimal Execution under Liquidity Uncertainty

[2506.11813] Optimal Execution under Liquidity Uncertainty Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantitative Finance > Mathematical Finance arXiv:2506.11813 (q-fin) [Submitted on 13 Jun 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: Optimal Execution under Liquidity Uncertainty Authors: Etienne Chevalier , Yadh Hafsi , Vathana Ly Vath , Sergio Pulido View a PDF of the paper titled Optimal Execution under Liquidity Uncertainty, by Etienne Chevalier and 3 other authors View PDF 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. We allow for general limit order book shapes to characterize instantaneous market impact. To model the resilience dynamics, we introduce a stochastic process that governs the rate at which the deviation between the impacted and unaffected prices decays. This volume-effect process reflects fluctuations in market activity that drive the pace of liquidity replenishment. 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. Subjects: Mathematical Finance (q-fin.MF) ; Trading and Market Microstructure (q-fin.TR) MSC classes: 93E20, 49L25, 91B70 Cite as: arXiv:2506.11813 [q-fin.MF] (or arXiv:2506.11813v2 [q-fin.MF] for this version) https://doi.org/10.48550/arXiv.2506.11813 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yadh Hafsi [ view email ] [v1] Fri, 13 Jun 2025 14:17:31 UTC (169 KB) [v2] Sat, 11 Apr 2026 09:53:59 UTC (157 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal Execution under Liquidity Uncertainty, by Etienne Chevalier and 3 other authors View PDF TeX Source view license Current browse context: q-fin.MF < prev | next > new | recent | 2025-06 Change to browse by: q-fin q-fin.TR References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Valuation and Selection Processes in Human Decision Making under Uncertainty#354132
• Robust Decision Making and Mechanism Design for Algorithmic Markets and Platforms#634778
• Amortized Asynchronous Byzantine Reliable Broadcast with Optimal Resilience#175200
• Optimiser la gestion des eaux de pluies et des eaux grises pour un quartier plus résilient#215327
• Permissible Promise-Making Under Uncertainty#748384