Portfolio Liquidation Games with Self-exciting Order Flow

Guanxing Fu, Ulrich Horst, Xiaonyu Xia

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1020-1065
Number of pages46
JournalMathematical Finance
Issue number4
Publication statusPublished - Oct 2022


  • Hawkes process
  • mean-field games
  • portfolio liquidation
  • singular terminal value
  • stochastic games

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics


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