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Portfolio Liquidation Games with Self-Exciting Order Flow

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  • Guanxing Fu
  • Ulrich Horst
  • Xiaonyu Xia

Abstract

We analyze novel portfolio liquidation games with self-exciting order flow. Both the N-player game and the mean-field game are considered. We assume that players' trading activities have an impact on the dynamics of future market order arrivals thereby generating an additional transient price impact. Given the strategies of her competitors each player solves a mean-field control problem. We characterize open-loop Nash equilibria in both games in terms of a novel mean-field FBSDE system with unknown terminal condition. Under a weak interaction condition we prove that the FBSDE systems have unique solutions. Using a novel sufficient maximum principle that does not require convexity of the cost function we finally prove that the solution of the FBSDE systems do indeed provide existence and uniqueness of open-loop Nash equilibria.

Suggested Citation

  • Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    • Handle: RePEc:arx:papers:2011.05589
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    References listed on IDEAS

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    Cited by:

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    2. Peter Bank & 'Alvaro Cartea & Laura Korber, 2023. "Optimal execution and speculation with trade signals," Papers 2306.00621, arXiv.org, revised Dec 2024.
    3. Eyal Neuman & Moritz Vo{ss}, 2021. "Trading with the Crowd," Papers 2106.09267, arXiv.org, revised Mar 2023.
    4. Moritz Voß, 2022. "A two-player portfolio tracking game," Mathematics and Financial Economics, Springer, volume 16, number 6, December.

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