Stochastic recursive optimal control problem of reflected stochastic differential systems. Issue 9 (1st September 2020)

• Record Type: Journal Article
• Authors: Feng, Xinwei
• Is Part Of: International journal of control. Volume 93:Issue 9(2020)
• Page Start: 2187
• Page End: 2198
• Publication Date: 2020-09-01
• Subjects: Stochastic recursive optimal control -- generalised reflected backward stochastic differential equations -- dynamic programming principle -- viscosity solution -- nonlinear Neumann boundary condition; 93E20 -- 60H99 -- 60H30 -- 35K86; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1550682
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: In this paper, we study one kind of stochastic recursive optimal control problem in which the control system is stochastic differential equations reflected in a domain and the cost functional is defined by generalised backward stochastic differential equations with reflection. We establish the dynamic programming principle for the value function and show that it is a viscosity solution of the associated obstacle problem for the corresponding Hamilton-Jacobi-Bellman equation with a nonlinear Neumann boundary condition.