Portfolio Liquidation Games with Self-Exciting Order Flow

TL;DR

This paper studies portfolio liquidation games incorporating self-exciting order flow, analyzing both N-player and mean-field game models, and characterizes Nash equilibria via novel FBSDE systems.

Contribution

It introduces a new mean-field FBSDE framework with unknown terminal conditions for modeling self-exciting order flow in liquidation games.

Findings

Unique solutions to the FBSDE systems under weak interaction conditions

Existence and uniqueness of open-loop Nash equilibria proved using a novel maximum principle

Characterization of equilibria in both N-player and mean-field settings

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.