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.