强化学习框架下跳跃扩散模型的美式期权定价OA

This paper develops a reinforcement learning approach for pricing American options under jump-diffusion models.The optimal control framework of reinforcement learning is extended to address the optimal stopping problem,from which the corresponding Hamilton-Jacobi-Bellman(HJB)equations are derived.The existence and uniqueness of solutions are rigorously established using the fixed-point theorem and a generalized extremum principle.A policy iteration numerical algorithm is proposed based on this theoretical foundation for numerical implementation,and its convergence properties and convergence rate are rigorously analyzed,with proofs provided by contradiction.Furthermore,a reinforcement learning algorithm is developed as a numerical pricing method.Numerical experiments across various jump-diffusion models and option types validate the effectiveness of the proposed algorithm in generating accurate pricing results,while demonstrating computational advantages,particularly in high-dimensional scenarios.The results establish a unified framework that combines theoretical guarantees with practical efficiency for pricing complex derivatives.