This was part of Applications to Financial Engineering

Portfolio liquidation under endogenous order flow – from single player models to mean-field games

Ulrich Horst, Humboldt University Berlin
Monday, December 6, 2021

Abstract: We consider single and multi-player portfolio liquidation models with self-exciting order flow in which a player’s trading activity has an impact of future order flow. The deterministic single player model is solved in closed form and calibrated to market data. Our empirical analysis shows that as the level of endogeneity increases, our strategy delivers increasingly superior performance to the commonly employed TWAP strategy. The general N-player and the mean-field game are solved within a common probabilistic framework. While the verification argument for the MFG is standard, the finite player models involve non-convex optimization problems and hence require novel verification arguments. We establish the existence of equilibria under a weak interaction condition and link the existence of statistical arbitrage to the strength of the permanent relative to the instantaneous market impact. The talk is based on two papers, one with Ying Chen and Hai Tran and one with Guanxing Fu and Xiaonyu Xia.