  To tackle the difficulties faced by both stochastic dynamic programming and
scenario tree methods, we present some variational approach for numerical
solution of stochastic optimal control problems. We consider two different
interpretations of the control problem, an algebraic and a functional one from
which we derive optimality conditions. An adaptative mesh discretization method
will be used to propose a tractable solution algorithm. An application to a
hydro-electric dam production management problem will be presented.
