标题：Relationship between backward and forward linear-quadratic mean-field-game with terminal constraint and optimal asset allocation for insurers and pension funds
作者：Du K.; Huang J.; Wu Z.
作者机构：[Du, K] School of Mathematics, Shandong University, Jinan, China, Zhongtai Securities Institute for Financial Study, Shandong University, Jinan, China 更多
通讯作者地址：[Wu, Z] School of Mathematics, Shandong UniversityChina;
来源：International Journal of Control
关键词：forward–backward stochastic differential equation; mean-field game; terminal constraint; ε-Nash equilibrium
摘要：Herein, motivated by problems faced by insurance firms, we consider the dynamic games of N weakly coupled linear forward stochastic systems with terminal constraints involving mean-field interactions. By penalisation method, the associated mean-field game (MFG) is formulated and its consistency condition is given by a fully coupled forward–backward stochastic differential equation (FBSDE). Moreover, the decentralised strategies are obtained, and the ε-Nash equilibrium is verified. In addition, we study the connection of backward linear quadratic (LQ) MFG and forward LQ MFG with terminal constraint. Furthermore, the decoupled optimal strategies of this MFG are solved explicitly by introducing some Riccati equations. As an illustration, some simulations of the optimal asset allocation for the firm and pension funds are further studied. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.