In this paper, we present a novel and computationally efficient approach to constrained discrete-time dynamic asset allocation over multiple periods. This technique is able to control portfolio expectation and variance at both final and intermediate stages of the decision horizon and may account for proportional transaction costs and intertemporal dependence of the return process. A key feature of the proposed method is the use of a linearly parameterized class of feedback control policies, which permits us to obtain explicit analytic expressions for the portfolio statistics over time. These expressions are proved to be convex in the decision parameters, and hence, under these control laws, the multistage problem is formulated and solved by means of efficient tools for quadratic or second-order-cone convex programming.