Applications of Stochastic Control Theory for Portfolio Optimization

The present work is devoted to investigating portfolio optimization. In the first part, we address the problem of robust utility maximization, where we consider the uncertainty in the drift and covariance matrix of the securities. In the second part, we aim at steering the portfolio wealth to a prescribed terminal distribution. We study this problem with the tools of optimal mass transport. We designed two deep neural network-based algorithms to solve optimal transport problems. The first deep learning algorithm is based on the penalization of the terminal constraint. In the second algorithm, we solve the dual problem with adversarial networks.