Risk-Sensitive Q-Learning in Continuous Time with Application to Dynamic Portfolio Selection

Chuhan Xie

Keywords: risk-sensitive, continuous time, reinforcement learning, stochastic control, dynamic portfolio selection

TL;DR: This paper proposes the problem of risk-sensitive reinforcement learning in continuous time, and establishes theoretical foundation and q-learning algorithms.

Abstract: This paper studies the problem of risk-sensitive reinforcement learning (RSRL) in continuous time, where the environment is characterized by a controllable stochastic differential equation (SDE) and the objective is a potentially nonlinear functional of cumulative rewards. We prove that when the functional is an optimized certainty equivalent (OCE), the optimal policy is Markovian with respect to an augmented environment. We also propose \textit{CT-RS-q}, a risk-sensitive q-learning algorithm based on a novel martingale characterization approach. Finally, we run a simulation study on a dynamic portfolio selection problem and illustrate the effectiveness of our algorithm.

Submission Number: 147