Linear Quadratic Stochastic Optimal Regulator With Positive Control

This paper is concerned with the stochastic linear quadratic optimal control problem with a positivity constraint on the control. The value function is shown to be lipschitz continuous in the time variable t, continuously differential and convex in the state variable x. Consequently, we prove that the value function is the strong solution of the HJB equa-tion(i.e.the value function satisfies the HJB equation almost everywhere). The optimal control is characterized via the partial derivative of the value function.