Portfolio liquidation games with self‐exciting order flow

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