Optimal continuous-singular control of stochastic McKean-Vlasov system in Wasserstein space of probability measures (Q2103058)

Summary: In this paper, we study the local form of maximum principle for optimal stochastic continuous-singular control of nonlinear Itô stochastic differential equation of McKean-Vlasov type, with incomplete information. The coefficients of the system are nonlinear and depend on the state process as well as its probability law. The control variable is allowed to enter into both drift and diffusion coefficients. The action space is assumed to be convex. The proof of our local maximum principle is based on the differentiability with respect to the probability law in Wasserstein space of probability measures with some appropriate estimates.