We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances while satisfying hard bounds on the control actions. We pose the problem of selecting an appropriate optimal controller on vector spaces of functions and show that the resulting optimization problem has a tractable convex solution. Under marginal stability of the zero-control and zero-noise system we synthesize receding horizon polices that ensure bounded variance of the states while enforcing hard bounds on the controls. We provide examples that illustrate the effectiveness of our control strategies, and how quantities needed in the formulation of the resulting optimization problems can be calculated off-line.