We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of optimality for two models. The first concerns the strict (classical) controls. The second is an extension of the first to relaxed controls, who are a measure valued processes.
Viscosity solutions to HJB equations associated with optimal control problem for McKean-Vlasov SDEs
Stochastic maximum principle for optimal control problem of backward systems with terminal condition in L1
A user's guide to 1D nonlinear backward stochastic differential equations with applications and open problems
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