Bringing Reinforcement Learning to Multi-Period Financial Planning: A Bridge Between Learning-Enabled and Stochastic Optimization

Abstract

Financial planning is rarely a one-shot decision: today’s saving, spending, and investment choices shape tomorrow’s wealth, liabilities, and goal attainment. This survey traces the mathematical evolution of multi-period financial planning over the past several decades, focusing on selected key methods ranging from classical stochastic optimization to learning-enabled decision systems. We begin with Markowitz’s single-period mean–variance optimization and trace the field’s evolution toward two major multi-period optimization paradigms: scenario-based approaches, such as multi-stage stochastic programming (MSP), and state-space approaches, including model-based dynamic programming (DP) and model-free reinforcement learning (RL). While traditional MSP and DP provide the mathematical backbone for sequential financial decision-making, their practical application has long been constrained by the curse of dimensionality, model misspecification, and restrictive assumptions required for tractability. Recent advances in model-free RL create new opportunities for adaptive and scalable sequential decision-making without relying on rigid transition models or handcrafted scenario trees. Building on this foundation, we review recent RL applications in multi-period financial planning for both individuals and institutions and classify the literature into three roles: hybrid RL, scalable RL, and end-to-end RL. Finally, we discuss the evolving landscape of AI/ML-driven automated investing, highlighting its promise for algorithmic financial planning as well as key challenges regarding data, interpretability, trust, and regulation.