OnpartiallyobservedoptimalstochasticcontrolofMcKean-Vlasovsystemsin Wasserstein space of probability measure swith applications

Abstract

This thesis presents two research topics about stochastic control problems of the general McKean–Vlasov equations, in which the coefficients depend nonlinearly on both the state process as well as its law. In the first topic, we establish partially observed necessary conditions of optimality for forward-backward stochastic differential equations driven by both a family of Teugels martingales and an independent Brownian motion under the assumption that the control domain is supposed to be convex. As an application of the general theory, a partially observed linear-quadratic control problem is studied in terms of stochastic filtering. The second topic is to study the maximum principle for the partially observed risk-sensitive optimal control problem of FBSDEs, and the cost functional is a McKean–Vlasov exponential of integral type. Moreover, un der certain concavity assumptions, we obtain the sufficient conditions of optimality. As an application, a linear-quadratic risk-sensitive optimal control problem under partially observed information and fully observed information is solved by using main results.