In this paper we develop a simulation-based approach to stochastic dynamic programming. To solve the Bellman equation we construct Monte Carlo estimates of Q-values. Our method is scalable to high dimensions and works in both continuous and discrete state and decision spaces while avoiding discretization errors that plague traditional methods. We provide a geometric convergence rate. We illustrate our methodology with a dynamic stochastic investment problem. Copyright © 2011 John Wiley & Sons, Ltd.