均衡Riccati方程的新进展
The Latest Development of Equilibrium Riccati Equation
DOI: 10.12677/ORF.2020.104030, PDF,    国家自然科学基金支持
作者: 张大永, 彭云飞：贵州大学数学与统计学院，贵州 贵阳
关键词: Riccati方程；均衡Riccati方程；时间不一致；Riccati Equation； Equilibrium Riccati Equation； Time-Inconsistent
摘要: 自Riccati方程被提出以来，一直是数学家关注的重要问题之一。其早期研究推动了微分方程的发展。20世纪中期，最优控制论发展使得Riccati方程大放异彩。特别地，时间不一致控制问题成为数学与金融的前沿交叉课题，Riccati方程再次引起许多学者的关注。本文基于时间不一致控制问题的最新进展和Riccati方程的研究历史，特别是Riccati方程与控制论的关系，详细综述了均衡Riccati方程的研究进展，由此展示Riccati方程将再次焕发新的活力。
Abstract: Riccati equation has been one of the most important issues for mathematicians since it was proposed. The prior research promoted the development of differential equations. Moreover, Riccati equation has been highly active owing to the development of optimal control theory in the Mid-20th century. In particular, the time-inconsistent control problem has become an interdisciplinary frontier of mathematics and finance, which makes such equation attract considerable attention of researchers again. Based on the latest development of time-inconsistent control and the history of Riccati equation research, especially the relation between Riccati equation and control theory, this paper surveys the research advance of equilibrium Riccati equation in detail. As a consequence, the Riccati equation is given a new vitality.
文章引用：张大永, 彭云飞. 均衡Riccati方程的新进展[J]. 运筹与模糊学, 2020, 10(4): 289-295. https://doi.org/10.12677/ORF.2020.104030

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