Deep Learning Algorithm to solve Portfolio Management with Proportional Transaction Cost

Portfolio selection with proportional transaction cost is a singular stochastic control problem that has been widely discussed. In this paper, we propose a deep learning based numerical scheme to solve transaction cost problems, and compare its effectiveness with a penalty partial differential equation (PDE) method. We further extend it to multi-asset cases which existing numerical methods can not be applied to due to the curse of dimensionality. Deep learning algorithm directly approximates the optimal trading strategies by a feedforward neural network at each discrete time. It is observed that deep learning approach can achieve satisfying performance to characterize optimal buy and sell boundaries and thus value function.