Linear‐Quadratic Stackelberg Game for Mean‐Field Backward Stochastic Differential System and Application

This paper is concerned with a new kind of Stackelberg differential game of mean‐field backward stochastic differential equations (MF‐BSDEs). By means of four Riccati equations (REs), the follower first solves a backward mean‐field stochastic LQ optimal control problem and gets the corresponding open‐loop optimal control with the feedback representation. Then the leader turns to solve an optimization problem for a 1 × 2 mean‐field forward‐backward stochastic differential system. In virtue of some high‐dimensional and complicated REs, we obtain the open‐loop Stackelberg equilibrium, and it admits a state feedback representation. Finally, as applications, a class of stochastic pension fund optimization problems which can be viewed as a special case of our formulation is studied and the open‐loop Stackelberg strategy is obtained.