Risk-Sensitive Q-Learning in Continuous Time with Application to Dynamic Portfolio Selection
This work addresses risk management in continuous-time decision-making, particularly for financial applications like portfolio selection, representing an incremental advancement in the field.
The paper tackles risk-sensitive reinforcement learning in continuous time by proving that the optimal policy is Markovian for optimized certainty equivalent objectives and proposing a novel q-learning algorithm, CT-RS-q, which is validated through simulations on a dynamic portfolio selection problem.
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.