Connection between MP and DPP for Stochastic Recursive Optimal Control Problems: Viscosity Solution Framework in Local Case

This paper deals with a nonsmooth version of the connection between the maximum principle and dynamic programming principle, for the stochastic recursive control problem when the control domain is convex. By employing the notions of sub- and super-jets, the set inclusions are derived among the value function and the adjoint processes. The general case for non-convex control domain is open.