  This paper analyzes the discretization of a Neumann boundary control problem
with a stochastic parabolic equation, where an additive noise occurs in the
Neumann boundary condition. The convergence is established for general
filtrations, and the convergence rate $ O(\tau^{1/4-\epsilon} +
h^{3/2-\epsilon}) $ is derived for the natural filtration of the Q-Wiener
process. A Monte-Carlo method to solve the discrete stochastic optimal control
problem is proposed.
