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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 (MFG) 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 open‐loop Nash equilibria.

Suggested Citation

  • Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "Portfolio liquidation games with self‐exciting order flow," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1020-1065, October.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:4:p:1020-1065
    DOI: 10.1111/mafi.12359
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    References listed on IDEAS

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