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

Kai Du and Zhen Wu

Mathematical Problems in Engineering, 2019, vol. 2019, 1-17

Abstract:

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 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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:1798585

DOI: 10.1155/2019/1798585

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