Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations

In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing new adjoint equation, establish sufficient verification theorem for optimal strategies leader and follower in general case. Then, focus on linear–quadratic (LQ) with delay. The equilibrium is presented generalized fully coupled anticipated forward–backward Equation (AFBSDDE), which composed (ASDEs) BSDDEs. Moreover, obtain unique solvability AFBSDDE using continuation method. As an application theoretical results, pension fund problem delay effect considered.