On optimal solutions of general continuous‐singular stochastic control problem of McKean‐Vlasov type

Abstract

In this paper, we establish general necessary optimality conditions for stochastic continuous‐singular control of McKean‐Vlasov type equations. The coefficients of the state equation depend on the state of the solution process as well as of its probability law and the control variable. The coefficients of the system are nonlinear and depend explicitly on the absolutely continuous component of the control. The control domain under consideration is not assumed to be convex. The proof of our main result is based on the first‐ and second‐order derivatives, with respect to measure in Wasserstein space of probability measures, and by using variational method.