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Portfolio selection is vulnerable to the error-amplifying effects of combining optimization with statistical estimation and model error. For dynamic portfolio control, sources of model error include the evolution of market factors and the influence of these factors on asset returns. We develop portfolio control rules that are robust to this type of uncertainty, applying a stochastic notion of robustness to uncertainty in model dynamics. In this stochastic formulation, robustness reflects uncertainty about the probability law generating market data, and not just uncertainty about model parameters. We analyze both finite-and infinite-horizon problems in a model in which returns are driven by factors that evolve stochastically. The model incorporates transaction costs and leads to simple and tractable optimal robust controls for multiple assets. We illustrate the performance of the controls on historical data. As one would expect, in-sample tests show no evidence of improved performance through robustness-evaluating performance on the same data used to estimate a model leaves no room to capture model uncertainty. However, robustness does improve performance in out-of-sample tests in which the model is estimated on a rolling window of data and then applied over a subsequent time period. By acknowledging uncertainty in the estimated model, the robust rules lead to less aggressive trading and are less sensitive to sharp moves in underlying prices.

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.