Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems

  • Jingrui Sun
  • Jiongmin Yong

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Jingrui Sun, Jiongmin Yong
    Pages 1-13
  3. Jingrui Sun, Jiongmin Yong
    Pages 15-67
  4. Jingrui Sun, Jiongmin Yong
    Pages 69-123
  5. Back Matter
    Pages 125-130

About this book


This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.


Linear-quadratic optimal control Two-person differential game Nash equilibrium Mean-field Riccati equation

Authors and affiliations

  • Jingrui Sun
    • 1
  • Jiongmin Yong
    • 2
  1. 1.Department of MathematicsSouthern University of Science and TechnologyShenzhenChina
  2. 2.Department of MathematicsUniversity of Central FloridaOrlandoUSA

Bibliographic information

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