Linear-Quadratic Pareto Cooperative Game for Mean-Field Backward Stochastic System  

作　　者：WANG Yu 

机构地区：[1]School of Control Science and Engineering,Shandong University,Jinan 250061,China

出　　处：《Journal of Systems Science & Complexity》2024年第3期947-964,共18页系统科学与复杂性学报（英文版）

基　　金：supported by the National Key R&D Program of China under Grant No. 2022YFA1006103;the National Natural Science Foundation of China under Grant Nos. 61821004, 61925306, and 11831010;the Natural Science Foundation of Shandong Province under Grant Nos. ZR2019ZD42 and ZR2020ZD24。

摘　　要：This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost functional. Based on a weighted sum optimality method, the Pareto game is equivalently converted to an optimal control problem. In the first place,the feedback form of Pareto optimal strategy is derived by virtue of decoupling technology, which is represented by four Riccati equations, a mean-field forward stochastic differential equation(MF-FSDE),and a mean-field backward stochastic differential equation(MF-BSDE). In addition, the corresponding Pareto optimal solution is further obtained. Finally, the author solves a problem in mathematical finance to illustrate the application of the theoretical results.

关 键 词：Backward stochastic differential equation linear-quadratic control MEAN-FIELD Pareto optimality 

分 类 号：O211.63[理学—概率论与数理统计]