Solving stochastic optimal control using 4 step scheme

In this paper, the authors solve the stochastic optimal control problem using the four step scheme, which is a systematic method to solve the forward backward stochastic differential equations (FBSDE). The stochastic optimal control problem linear quadratic (stochastic LQ) problem is studied using the Pontryagin's type maximum principle(MP), which results FBSDE from which we could retrieve the famous stochastic Riccati equation. Finally, they reveal the strong relation between the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) driven from the dynamic programming method (DP), and the partial differential equation driven from the 4-step scheme.