CONTROLLED REFLECTED SDES AND NEUMANN PROBLEM FOR BACKWARD SPDES

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Qiu, Jinniao
• 署名单位: University of Michigan System; University of Michigan; University of Calgary
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1465
• 发表日期: 2019
• 页码: 2819-2848
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; MAXIMUM PRINCIPLE

摘要

We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial differential equation (BSPDE) with Neumann boundary conditions. We prove the existence and uniqueness of a sufficiently regular solution for this BSPDE, which is then used to construct the optimal feedback control. In fact, we prove a more general result: the existence and uniqueness of strong solution for the Neumann problem for general nonlinear BSPDEs, which might be of interest even out of the current context.