On 'predicted miss' stochastic control problems

For steering a linear stochastic system with bounded controls so as to be as close as possible to a given hyperplane at the terminal time, Benes proved that the controller that predicts which side of the hyperplane the state would be on with no further control, and then applies full “bang” in the appropriate direction, optimal, a result conjectured y Hilborn. In this paper a different proof of this result is presented, using martingale-based optimality criteria.