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Trading with the crowd

Author

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  • Eyal Neuman
  • Moritz Voß

Abstract

We formulate and solve a multi‐player stochastic differential game between financial agents who seek to cost‐efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with taking into account a common general price predicting signal. The unique Nash‐equilibrium strategies reveal how each agent's liquidation policy adjusts the predictive trading signal to the aggregated transient price impact induced by all other agents. This unfolds a quantitative relation between trading signals and the order flow in crowded markets. We also formulate and solve the corresponding mean field game in the limit of infinitely many agents. We prove that the equilibrium trading speed and the value function of an agent in the finite N‐player game converges to the corresponding trading speed and value function in the mean field game at rate O(N−2)$O(N^{-2})$. In addition, we prove that the mean field optimal strategy provides an approximate Nash‐equilibrium for the finite‐player game.

Suggested Citation

  • Eyal Neuman & Moritz Voß, 2023. "Trading with the crowd," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 548-617, July.
    • Handle: RePEc:bla:mathfi:v:33:y:2023:i:3:p:548-617
    DOI: 10.1111/mafi.12390
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    References listed on IDEAS

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    8. Olivier F'eron & Peter Tankov & Laura Tinsi, 2020. "Price formation and optimal trading in intraday electricity markets with a major player," Papers 2011.07655, arXiv.org.
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    10. Eyal Neuman & Moritz Vo{ss}, 2020. "Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact," Papers 2002.09549, arXiv.org, revised Jan 2022.
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    Citations

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    Cited by:

    1. Eduardo Abi Jaber & Eyal Neuman, 2025. "Optimal Liquidation with Signals: the General Propagator Case," Post-Print hal-03835948, HAL.
    2. Eduardo Abi Jaber & Alessandro Bondi & Nathan De Carvalho & Eyal Neuman & Sturmius Tuschmann, 2025. "Fredholm Approach to Nonlinear Propagator Models," Papers 2503.04323, arXiv.org.
    3. Guanxing Fu & Paul P. Hager & Ulrich Horst, 2024. "A Mean-Field Game of Market Entry: Portfolio Liquidation with Trading Constraints," Papers 2403.10441, arXiv.org, revised Jul 2025.
    4. Guanxing Fu & Paul Hager & Ulrich Horst, 2024. "A Mean-Field Game of Market Entry," Rationality and Competition Discussion Paper Series 517, CRC TRR 190 Rationality and Competition.
    5. Rama Cont & Alessandro Micheli & Eyal Neuman, 2025. "Fast and slow optimal trading with exogenous information," Finance and Stochastics, Springer, vol. 29(2), pages 553-607, April.
    6. Eduardo Abi Jaber & Eyal Neuman & Moritz Voss, 2023. "Equilibrium in Functional Stochastic Games with Mean-Field Interaction," Working Papers hal-04119787, HAL.
    7. Steven Campbell & Marcel Nutz, 2025. "Optimal Execution among $N$ Traders with Transient Price Impact," Papers 2501.09638, arXiv.org.
    8. Alexander Barzykin & Robert Boyce & Eyal Neuman, 2024. "Unwinding Toxic Flow with Partial Information," Papers 2407.04510, arXiv.org.
    9. 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.
    10. Steven Campbell & Marcel Nutz, 2025. "Randomization in Optimal Execution Games," Papers 2503.08833, arXiv.org.

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