International Journal of Control, Vol.93, No.9, 2187-2198, 2020
Stochastic recursive optimal control problem of reflected stochastic differential systems
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.
Keywords:Stochastic recursive optimal control;generalised reflected backward stochastic differential equations;dynamic programming principle;viscosity solution;nonlinear Neumann boundary condition