FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND LINEAR-QUADRATIC GENERALIZED STACKELBERG GAMES

摘要

A multilevel self-similar domination-monotonicity structure is proposed, and a kind of coupled forward-backward stochastic differential equations (FBSDEs) with such structure is proved to be uniquely solvable. Then, this kind of FBSDEs is used to characterize the unique equilibrium of a linear-quadratic generalized Stackelberg game with multilevel hierarchy in a closed form.