  In this paper we propose a new methodology for solving an uncertain
stochastic Markovian control problem in discrete time. We call the proposed
methodology the adaptive robust control. We demonstrate that the uncertain
control problem under consideration can be solved in terms of associated
adaptive robust Bellman equation. The success of our approach is to the great
extend owed to the recursive methodology for construction of relevant
confidence regions. We illustrate our methodology by considering an optimal
portfolio allocation problem, and we compare results obtained using the
adaptive robust control method with some other existing methods.
