不对称信息下的主从随机微分对策理论及其应用

This project aims to research the leader-follower stochastic differential games with asymmetric information, also known as Stackelberg games, who involves players with asymmetric roles, the leaders and the followers. Usually the leaders and the followers have asymmetric informations, which have profound applications background in finance, engineering and economical management. Leader-follower stochastic differential games have close connection with forward-backward stochastic differential equations, stochastic optimal control problems of mean-field type, and stochastic state filtering theory. Our target in this project is to apply Pontraygin’s maximum principle and stochastic filtering approaches to solve several kinds of leader-follower stochastic differential games, including the white-noise observation model with asymmetric information, partial state observation models, time-delayed models, etc. Moreover, we wish to apply the above theoretical results to seek open-loop and close-loop Stackelberg equilibria for linear-quadratic leader-follower stochastic differential games with asymmetric information. Combining with the empirical data in financial market and engineering management, and applying numerical computation and statistical method, we wish to provide rational reference for the practitioners in finance, engineering and management.

本项目系统研究不对称信息下的主从随机微分对策（又称作Stackelberg对策），对策参与者具有不同的角色：主导者与跟从者。通常主导者与跟从者拥有不对称的信息，这一问题在金融、工程与经济管理科学中有着广泛的应用背景。主从随机微分对策与正倒向随机微分方程、平均场随机最优控制问题以及随机状态滤波理论有着密切联系。本项目旨在应用Pontryagin最大值原理和随机滤波技术，解决几类主从随机微分对策问题，包括不对称信息下的白噪声观测模型、部分状态观测模型与时间延迟模型等；并进一步利用上述理论结果寻求不对称信息的线性二次主从随机微分对策问题的开环和闭环Stackelberg均衡策略，结合金融市场和工程管理中的实证数据，运用数值计算和统计方法，为金融、工程和经济管理领域从业者的理性决策提供合理的参考依据。

本项目研究了不对称信息下的主从随机微分对策问题，对策的参与者：主导者与跟从者，拥有不对称的信息。主从随机微分对策与正倒向随机微分方程、平均场随机最优控制问题以及随机状态滤波理论有着密切联系。本项目在执行的几年时间里，主要应用Pontryagin最大值原理和随机滤波技术，解决了几类主从随机微分对策问题，包括不对称信息下的白噪声观测模型、重叠信息下的白噪声观测模型、倒向随机系统的不对称信息模型、带观测的随机模型、时间延迟模型等，进一步利用理论结果寻求不对称信息的线性二次主从随机微分对策问题的Stackelberg均衡策略，取得了一批理论成果，推动了随机最优控制和微分对策领域的发展。