Well-posedness of Stochastic Riccati Equations and Closed-Loop Solvability for Stochastic Linear Quadratic Optimal Control Problems

Qi Lü

Published 2018-11-18, updated 2019-01-18Version 2

We study the closed-loop solvability of a stochastic linear quadratic optimal control problem for systems governed by stochastic evolution equations. This solvability is established by means of solvability of the corresponding Riccati equation, which is implied by the uniform convexity of the quadratic cost functional. At last, conditions ensuring the uniform convexity of the cost functional are discussed.