同济大学学报（自然科学版）2026，Vol.54Issue(6)：950-962,13.DOI:10.11908/j.issn.0253-374x.25115
强化学习框架下跳跃扩散模型的美式期权定价
American Option Pricing in Jump-Diffusion Models Under Reinforcement Learning Framework
摘要
Abstract
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.关键词
美式期权定价/强化学习/跳跃扩散模型/含非局部项非线性方程Key words
American option pricing/reinforcement learning/Jump-diffusion model/nonlinear equations with non-local terms分类
管理科学引用本文复制引用
董玉超,左乘风..强化学习框架下跳跃扩散模型的美式期权定价[J].同济大学学报（自然科学版）,2026,54(6):950-962,13.基金项目
国家自然科学基金面上项目(12471425) （12471425）
