VISCOSITY SOLUTIONS TO SECOND ORDER PATH-DEPENDENT HAMILTON-JACOBI-BELLMAN EQUATIONS AND APPLICATIONS

• 成果类型: Article
• 署名作者: Zhou, Jianjun
• 署名单位: Northwest A&F University - China
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1954
• 发表日期: 2023
• 页码: 5564-5612
• 关键词: optimal stochastic-control; differential-equations; infinite dimensions; adapted solution; pdes; SPACES

摘要

In this article a notion of viscosity solutions is introduced for second -order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions and satisfies a stability property. Applications to backward stochastic Hamilton-Jacobi-Bellman equations are also given.