Global solutions of stochastic Stackelberg differential games under convex control constraint

This paper is concerned with a Stackelberg stochastic differential game, where the systems are driven by equation (SDE for short), in which control enters randomly disturbed coefficients (drift and diffusion). The region postulated to be convex. By making use of first-order adjoint (backward equation, BSDE we able establish Pontryagin’s maximum principle leader’s global solution, within adapted open-loop structure closed-loop memoryless information one, respectively, term indicates that domination over entire game duration. Since follower’s turns out BSDE, leader will confronted problem state kind fully coupled forward–backward (FBSDE short). As an application, study class linear–quadratic (LQ short) games process constrained closed convex subset Γ full space Rm. equations represented FBSDEs projection operators on Γ. means monotonicity condition method, existence uniqueness such obtained. When domain space, derive resulting backward Riccati equations.