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Fast and slow optimal trading with exogenous information

Author

Listed:
  • Rama Cont

    (University of Oxford)

  • Alessandro Micheli

    (Imperial College London)

  • Eyal Neuman

    (Imperial College London)

Abstract

We model the interaction between an investor executing trades at low frequency and a high-frequency trader as a multiperiod stochastic Stackelberg game. The high-frequency trader exploits price information more frequently and is subject to periodic inventory constraints. We are able to explicitly compute the equilibrium strategies, in two steps. We first derive the optimal strategy of the high-frequency trader given any strategy adopted by the investor. Then we solve the problem of the investor given the optimal strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation. Our results show that the high-frequency trader adopts a predatory strategy whenever the value of the trading signal is high, and follows a cooperative strategy otherwise. We also show that there is a net gain in performance for the investor from taking into account the order flow of the high-frequency trader. A U-shaped intraday pattern in trading volume is shown to arise endogenously as a result of the strategic behaviour of the agents.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:29:y:2025:i:2:d:10.1007_s00780-025-00560-w
    DOI: 10.1007/s00780-025-00560-w
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    References listed on IDEAS

    as
    1. Wood, Robert A & McInish, Thomas H & Ord, J Keith, 1985. "An Investigation of Transactions Data for NYSE Stocks," Journal of Finance, American Finance Association, vol. 40(3), pages 723-739, July.
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    4. Chen, Marie & Garriott, Corey, 2020. "High-frequency trading and institutional trading costs," Journal of Empirical Finance, Elsevier, vol. 56(C), pages 74-93.
    5. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
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    12. Alessandro Micheli & Johannes Muhle-Karbe & Eyal Neuman, 2021. "Closed-Loop Nash Competition for Liquidity," Papers 2112.02961, arXiv.org, revised Jun 2023.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Market microstructure; High-frequency trading; Optimal stochastic control; Stochastic games; Price impact; Fredholm integral equations; Trading signals; Stackelberg equilibrium;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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