Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions

Jingrui Sun received his PhD in Mathematics from the University of Science and Technology of China in 2015. From 2015 to 2017, he was a Postdoctoral Fellow at the Hong Kong Polytechnic University and then a Research Fellow at the National University of Singapore. From 2017 to 2018, he was a Visiting Assistant Professor at the University of Central Florida, USA. Since the spring of 2019, he has been an Assistant Professor at the Southern University of Science and Technology, China. Dr. Sun has broad interests in the area of control theory and its applications. Aside from his primary research on stochastic optimal control and differential games, he is exploring forward and backward stochastic differential equations, stochastic analysis, and mathematical finance. Jiongmin Yong received his PhD from Purdue University in 1986 and is currently a Professor of Mathematics at the University of Central Florida, USA. His main research interests include stochastic control, stochastic differential equations, and optimal control of partial differential equations. Professor Yong has co-authored the following influential books: “Stochastic Control: Hamiltonian Systems and HJB Equations” (with X. Y. Zhou, Springer 1999), “Forward-Backward Stochastic Differential Equations and Their Applications” (with J. Ma, Springer 1999), and “Optimal Control Theory for Infinite-Dimensional Systems” (with X. Li, Birkhauser 1995). His current interests include time-inconsistent stochastic control problems.

“This book offers results on the optimal control of a solution to the linear stochastic differential equation with a quadratic cost functional. ... This book is characterized by clear statements of problems, definitions, propositions, and theorems. It contains examples and counterexamples that support the theoretical results.” (Konstantin Rybakov, Mathematical Reviews, May, 2024)

• 1 introduction.- 2 Linear-Quadratic Optimal Controls in Finite Horizons.- 3 Linear-Quadratic Optimal Controls in Infinite Horizons.- 4 Linear Algebra and BSDEs.