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Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems (Paperback, 1st ed. 2020)
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Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems (Paperback, 1st ed. 2020)
Series: SpringerBriefs in Mathematics
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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.
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