Stochastic Linear Quadratic Optimal Control Theory: Open Loop and Closed Loop Solutions 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 the results in the context of finite and infinite horizon problems and discusses a number of new and interesting issues. Further it precisely identifies for the first time the interconnections between three well known relevant issues – the existence of optimal controls solvability of the optimality system and solvability of the associated Riccati equation. 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. 1 introduction 2 Linear Quadratic Optimal Controls in Finite Horizons 3 Linear Quadratic Optimal Controls in Infinite Horizons 4 Linear Algebra and BSDEs.