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A Simple Strategy to Deal with Toxic Flow

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  • 'Alvaro Cartea
  • Leandro S'anchez-Betancourt

Abstract

We model the trading activity between a broker and her clients (informed and uninformed traders) as an infinite-horizon stochastic control problem. We derive the broker's optimal dealing strategy in closed form and use this to introduce an algorithm that bypasses the need to calibrate individual parameters, so the dealing strategy can be executed in real-world trading environments. Finally, we characterise the discount in the price of liquidity a broker offers clients. The discount strikes the optimal balance between maximising the order flow from the broker's clients and minimising adverse selection losses to the informed traders.

Suggested Citation

  • 'Alvaro Cartea & Leandro S'anchez-Betancourt, 2025. "A Simple Strategy to Deal with Toxic Flow," Papers 2503.18005, arXiv.org.
    • Handle: RePEc:arx:papers:2503.18005
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    References listed on IDEAS

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    1. Etienne Chevalier & Yadh Hafsi & Vathana Ly Vath, 2024. "Optimal Execution under Incomplete Information," Papers 2411.04616, arXiv.org.
    2. Philippe Bergault & Leandro S'anchez-Betancourt, 2024. "A Mean Field Game between Informed Traders and a Broker," Papers 2401.05257, arXiv.org.
    3. Butz, M. & Oomen, R., 2019. "Internalisation by electronic FX spot dealers," LSE Research Online Documents on Economics 90485, London School of Economics and Political Science, LSE Library.
    4. 'Alvaro Cartea & Sebastian Jaimungal & Leandro S'anchez-Betancourt, 2024. "Nash Equilibrium between Brokers and Traders," Papers 2407.10561, arXiv.org, revised Jul 2024.
    5. Alexander Barzykin & Philippe Bergault & Olivier Guéant, 2023. "Algorithmic market making in dealer markets with hedging and market impact," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 41-79, January.
    6. M. Butz & R. Oomen, 2019. "Internalisation by electronic FX spot dealers," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 35-56, January.
    7. Alexander Barzykin & Robert Boyce & Eyal Neuman, 2024. "Unwinding Toxic Flow with Partial Information," Papers 2407.04510, arXiv.org.
    8. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    9. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    10. Martin Herdegen & Johannes Muhle-Karbe & Florian Stebegg, 2023. "Liquidity Provision with Adverse Selection and Inventory Costs," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1286-1315, August.
    11. Alif Aqsha & Fayc{c}al Drissi & Leandro S'anchez-Betancourt, 2024. "Strategic Learning and Trading in Broker-Mediated Markets," Papers 2412.20847, arXiv.org.
    12. Alessandro Micheli & Johannes Muhle-Karbe & Eyal Neuman, 2021. "Closed-Loop Nash Competition for Liquidity," Papers 2112.02961, arXiv.org, revised Jun 2023.
    13. Albert S. Kyle, 1989. "Informed Speculation with Imperfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 317-355.
    14. Alessandro Micheli & Johannes Muhle‐Karbe & Eyal Neuman, 2023. "Closed‐loop Nash competition for liquidity," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1082-1118, October.
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