Research on long-term behavior of control systems seems very important in many fields of applications. Our study is focused on two main impact sources: uncertainty and time preference of decision makers. We use the framework of stochastic LQ control theory to handle a variety of problems arisen from that consideration. The dynamics is linear in state and control, the diffusion matrix is time-varying (possibly unbounded, decreasing or constant). The quadratic cost includes discount function which represents different types of time preference (positive, zero or negative). By extending the notion of long-run average, a new criterion to be introduced in order to obtain an optimal control law. It relates to the problem of average optimality over an infinite-time horizon. Then proceeding to the issue of pathwise optimality we consider the random difference between the cost corresponding to the optimal feedback and the cost of any admissible control. A deterministic upper function of such a deficiency process serves as a risk evaluation measure if the average optimal control is applied. We obtain the unified upper function for a family of deficiency processes and establish its dependence on disturbance parameters and discounting.