Some recent developments in stochastic linear-quadratic optimal control

In this paper, we present an overview of recent developments in stochastic linear-quadratic optimal control, integrating the latest relevant works of the authors and their collaborators. The paper is structured into three closely related sections: stochastic linear-quadratic optimal control in finite time horizons, its counterpart in infinite time horizons, and an examination of the turnpike 性质 within stochastic linear-quadratic optimal control.