Reinforcement learning (RL) approach is widely used in control theory as an important method in the field of artificial intelligence. In control theory, stochastic models are used to simulate financial market models. Therefore, problems such as stock prediction and risk assessment in financial field can be transformed into optimization and control problems. RL problems are closely related to optimal control problems. Most traditional optimal control methods require complete knowledge of the system model, which has significant limitations. RL can be trained directly from data without models to obtain optimal value functions and optimal policies, and policy iteration provides a way to continuously improve performance.

This article investigates the infinite horizon optimal control problem for stochastic Markovian jump systems with Wiener and Poisson noises. First, a new policy iteration algorithm is designed by using integral reinforcement learning approach and subsystems transformation technique, which obtains the optimal solution without solving stochastic coupled algebraic Riccati equation (SCARE) directly. Second, through the transformation and substitution of the SCARE and feedback gain matrix, a policy iteration algorithm is devised to determine the optimal control strategy. This algorithm leverages only state trajectory information to obtain the optimal solution, and is updated in an unfixed form. Additionally, the algorithm remains unaffected by variations in Poisson jump intensity. Finally, an numerical example is given to verify the effectiveness and convergence of the proposed algorithms.