  Generalising the idea of the classical EM algorithm that is widely used for
computing maximum likelihood estimates, we propose an EM-Control (EM-C)
algorithm for solving multi-period finite time horizon stochastic control
problems. The new algorithm sequentially updates the control policies in each
time period using Monte Carlo simulation in a forward-backward manner; in other
words, the algorithm goes forward in simulation and backward in optimization in
each iteration. Similar to the EM algorithm, the EM-C algorithm has the
monotonicity of performance improvement in each iteration, leading to good
convergence properties. We demonstrate the effectiveness of the algorithm by
solving stochastic control problems in the monopoly pricing of perishable
assets and in the study of real business cycle.
