A General Maximum Principle for Delayed Stochastic Optimal Control Problems

In this paper, we consider optimal control problems derived by stochastic systems with distributed (average) and pointwise time delays, where control domains are non-convex and the diffusion coefficients depend on control variables. A general maximum principle is established for the underlying systems. To illustrate the theoretical result, the authors also work out two examples of delayed stochastic optimal control problems, and find the explicit expressions of the corresponding optimal control.