Extended MF-FBSDEs with nonlinear domination-monotonicity conditions and stochastic optimal controls of Linear System with quadruple controls

Abstract

This paper extends the domination-monotonicity conditions, which guarantee the well-posedness of extended mean-filed forward-backward stochastic differential equations (extended MF-FBSDEs), from the previously studied linear framework to a nonlinear setting by incorporating nonlinear adjoint functions. Utilizing this generalized well-posedness result for extended MF-FBSDEs in conjunction with other refined analytical techniques, we address two classes of stochastic quadruple optimal controlled problems: a linear-convex problem and a linear-quadratic problem with input constraints that are permitted to be time-dependent and random. For each problem, we establish the existence and uniqueness of optimal controls and derive their explicit closed-form representations.