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

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  • Kai Du
  • Zhen Wu

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.

Suggested Citation

  • Kai Du & Zhen Wu, 2019. "Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-17, February.
    • Handle: RePEc:hin:jnlmpe:1798585
    DOI: 10.1155/2019/1798585
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    Cited by:

    1. Yueyang Zheng & Jingtao Shi, 2020. "A Stackelberg Game of Backward Stochastic Differential Equations with Applications," Dynamic Games and Applications, Springer, vol. 10(4), pages 968-992, December.
    2. Wang, Guangchen & Wang, Wencan & Yan, Zhiguo, 2021. "Linear quadratic control of backward stochastic differential equation with partial information," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    3. Wang, Yu & Yan, Zhiguo, 2023. "Pareto-based Stackelberg differential game for stochastic systems with multi-followers," Applied Mathematics and Computation, Elsevier, vol. 436(C).

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