SDELP-DDPG: Stochastic differential equations with Lévy processes-driven deep deterministic policy gradient for portfolio management

Abstract

Portfolio management (PM) involves the ongoing redistribution of funds among various financial products, aiming to seek a balance between returns and risks. In this paper, we propose SDELP-DDPG, a novel approach to portfolio management that combines stochastic differential equations (SDEs) with Lévy processes and the deep deterministic policy gradient (DDPG) technique. To alleviate the challenges posed by exploration limitations and enhance the stability of DDPG, we employ SDEs driven by Lévy processes, with drift and diffusion coefficients represented by convolutional neural networks, to generate action policies. Additionally, we devise a reward function, which considers relative entropy, to guide RL agents in learning imitation policies using DDPG. Moreover, we incorporate an attention mechanism and the Ornstein–Uhlenbeck process to choose optimal actions. Our proposed algorithm is evaluated on three real-world datasets: the Dow Jones Industrial Average markets, the Energy markets and the cryptocurrency markets, and the experimental results validate the effectiveness of SDELP-DDPG compared to existing PM approaches.