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

Abstract EN

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.