Deep learning solution to mean field game of optimal liquidation

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 that employs two sub-networks to approximate solutions to the relevant partial differential equations. Our method adheres to the requirements of differential operators and satisfies both initial and terminal conditions through simultaneous training. A key advantage of our approach is its mesh-free nature, which mitigates the curse of dimensionality encountered in traditional numerical methods. We validate the effectiveness of our approach through numerical experiments on multi-dimensional portfolio liquidation models.