Reinforcement Learning for Dividend Optimization in Partially Observed Regime-Switching Diffusion Model

Abstract: This paper studies the optimal dividend problem with a bounded payout rate in a partially observed regime-switching diffusion model, where, in practice, the market regime is unobserved and key model parameters are unknown. To address this partial-information setting, we propose a continuous-time reinforcement learning (RL) approach within an exploratory (entropy-regularized) stochastic control framework for discounted dividends under regime switching. The associated exploratory Hamilton-Jacobi-Bellman (HJB) system admits semi-analytical characterizations of the value function and the optimal exploratory dividend policy, determined by two unknown functions solving two ordinary differential equations (ODEs) together with positive real roots of the induced quadratic equations. Exploiting this structure, we introduce parametric families for both the value function and the policy, using low-degree polynomial approximations to the ODE solutions. We then develop an actor-critic RL algorithm to learn the optimal exploratory policy through interactions with the market environment: it performs belief-state filtering from observed data and iterates policy evaluation and policy improvement online to refine the policy. Numerical experiments demonstrate strong out-of-sample performance of the learned dividend policies.