A robustness result for stochastic control

The solution of a stochastic control problem depends on the underlying model, i.e., on the probability measure induced by the model. The real world model may not be known precisely, and so one solves the problem for a hypothetical model that induces a measure generally different but close to the real one. We investigate two ways to derive a bound on the suboptimality of the hypothetical optimal control when it is used in the real problem. Both bounds are in terms of the Radon-Nikodym derivative of the real world measure with respect to the hypothetical one