Portfolio Liquidation Games with Self-Exciting Order Flow

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.

Trading with the Crowd

“…In our setting the source of randomness is a common noise, which is the exogenous signal. Moreover the convergence results in Fu et al [15] do not derive the convergence rate.…”

“…Finally some additional convergence results on a finite player game to a mean field game were derived recently for liquidation games with self-exciting order flow by Fu et al [15], which did not include a price predicting signal. These convergence results are quite different than the convergence results in this paper, as they derive the convergence of a game with stochastic i.i.d.…”

A two-player portfolio tracking game

“…Other recent work on both finite-player as well as infinite-player mean field price impact games with Almgren-Chriss type price impact include, e.g., Cardaliaguet and Lehalle [8], Huang et al [23], Casgrain and Jaimungal [12,13], Fu et al [21], Fu and Horst [19], Evangelista and Thamsten [18], and Drapeau et al [15], where finitely and infinitely many agents pursue optimal liquidation of their initial positions and interact through common aggregated permanent and temporary price impact. Price impact games of liquidating agents in a market model with transient price impact are analyzed, e.g., in Luo and Schied [24], Schied and Zhang [30], Schied et al [31], Strehle [34]; and very recently in Fu et al [20] and Neuman and Voß [27]. However, these works are all portfolio liquidation games where the agents steer their initial portfolio positions towards zero (with strict liquidation constraints enforced in [18][19][20][21]).…”

“…Price impact games of liquidating agents in a market model with transient price impact are analyzed, e.g., in Luo and Schied [24], Schied and Zhang [30], Schied et al [31], Strehle [34]; and very recently in Fu et al [20] and Neuman and Voß [27]. However, these works are all portfolio liquidation games where the agents steer their initial portfolio positions towards zero (with strict liquidation constraints enforced in [18][19][20][21]). In particular, the agents neither track any individual stochastic running trading targets nor do they aim for reaching an individual random terminal target position.…”

“…Fig.1Exemplary illustration of the weight functions w 1 , w 2 , w 3 , w 4 , w 5 on [0, T ] defined in(20). The parameters are T = 5, σ = 1, λ = 1, as well as γ = 4 (left panel), γ = 0.2 (right panel)…”