A General Stochastic Maximum Principle for Mean-Field Controls with Regime Switching

Focusing on regime-switching diffusions with mean-fields interactions, this paper is devoted to obtaining a general maximum principle. A main feature is that conditional mean-field is used in the controlled dynamic systems and the optimization process. Analysis of variational and adjoint equations using forward and backward stochastic differential equations with regime-switching and conditional mean-field is carried out. Necessary conditions for optimality are obtained without assuming the convexity of the control space. An example on conditional mean-variance portfolio selection with regime switching is given to illustrate the sufficient conditions for optimality.