An optimal control problem for functional forward-backward stochastic   systems and related Path-dependent HJB equations
  In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming principle and the related Path-dependent Hamilton-Jacobi-Bellman (HJB) equation in the framework of functional It\^o calculus. The stochastic verification theorem for the smooth case is proved. Finally, we show that the value function is the viscosity solution of the Path-dependent HJB equation. 
Shaolin Ji, Shuzhen Yang
math.PR math.OC