Deep Learning Solution to Mean Field Game of Optimal Liquidation

Abstract

This paper addresses optimal portfolio liquidation using mean field games (MFGs) and presents a solution method to tackle high-dimensional challenges. We develop a deep learning approach with two sub-networks to approximate solutions to the relevant partial differential equations. Our method adheres to differential operator requirements and satisfies initial and terminal conditions through simultaneous training. A significant advantage is its mesh-free nature, which alleviates the curse of dimensionality in traditional numerical methods. We validate our approach's effectiveness through numerical experiments on multi-dimensional portfolio liquidation models.

Keywords: Deep learningDeep Galerkin methodhigh-dimensionalityMean field gamesOptimal liquidation