A General Neural Network Methodology for Multi-period Portfolio Optimization

Abstract

In this thesis, we propose a neural network methodology for solving the multi-period portfolio optimization problem. Our approach formulates the problem as a stochastic optimal control problem and uses a single neural network model to approximate the optimal control function so that the optimal control can be obtained via solving a single standard optimization problem. Unlike traditional dynamic programming methods, our methodology eliminates the need for high-dimensional expectation evaluations, making it computationally efficient. Moreover, our framework is flexible and not restricted to specific objective functions or data models, allowing it to handle a wide range of portfolio optimization problems. In addition, by designing novel neural network models with suitable activation layers, we ensure that the neural network representation is always a feasible solution to the original optimal control problem so that the complex constrained portfolio optimization problems are converted into computationally feasible unconstrained ones. Furthermore, we provide mathematical proofs that our proposed neural network models are capable of approximating the constrained optimal control arbitrarily well, illustrating the validity and effectiveness of our approach. Finally, through extensive numerical experiments, we demonstrate the empirical performance of our methodology, validating its practical relevance and effectiveness in real-world investment decision-making.