Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 620-637.

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Linear-Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations with Jumps

Maoning Tang(),Qingxin Meng*()   

  1. College of Science, Huzhou University, Zhejiang Huzhou 313000
  • Received:2016-12-09 Online:2019-06-26 Published:2019-06-27
  • Contact: Qingxin Meng;
  • Supported by:
    the NSFC(11871121);the Natural Science Foundation of Zhejiang Province for Distinguished Young Scholar(LR15A010001)


This paper is concerned with a linear quadratic optimal control problem for meanfield backward stochastic differential equations driven by a Poisson random martingale measure and a Brownian motion. Firstly, by the classic convex variation principle, the existence and uniqueness of the optimal control is obtained. Secondly, the optimal control is characterized by the stochastic Hamilton system which turns out to be a linear fully coupled mean-field forward-backward stochastic differential equation with jumps by the duality method. Thirdly, in terms of a decoupling technique, the stochastic Hamilton system is decoupled by introducing two Riccati equations and a MF-BSDE with jumps. Then an explicit representation for the optimal control is obtained.

Key words: Mean-field, Optimal control, Backward stochastic Differential equation, Adjoint process

CLC Number: 

  • O232