Optimal multi-period leverage-constrained portfolios: A neural network approach

We present a neural network approach for multi-period portfolio optimization that relaxes the long-only restriction and instead imposes a bound constraint on leverage. We formulate the optimization problem for such a relaxed-constraint portfolio as a multi-period stochastic optimal control problem. We propose a novel relaxed-constraint neural network (RCNN) model to approximate the optimal control. Using our proposed RCNN model transforms the original leverage-constrained optimization problem into an unconstrained one, which makes solving it computationally more feasible. We prove mathematically that the proposed RCNN control model can approximate the optimal relaxed-constraint strategy with arbitrary precision. We further propose to compute the optimal outperforming strategy over a benchmark based on cumulative quadratic shortfall (CS). Using U.S. historical market data from Jan 1926 to Jan 2023, we computationally compare and assess the proposed neural network approach to the optimal leverage-constrained strategy and long-only strategy respectively. We demonstrate that the leverage-constrained optimal strategy can achieve enhanced performance over the long-only strategy in outperforming a benchmark portfolio.