  We consider the numerical solution of Hamilton-Jacobi-Bellman equations
arising in stochastic control theory. We introduce a class of monotone
approximation schemes relying on monotone interpolation. These schemes converge
under very weak assumptions, including the case of arbitrary degenerate
diffusions. Besides providing a unifying framework that includes several known
first order accurate schemes, stability and convergence results are given,
along with two different robust error estimates. Finally, the method is applied
to a super-replication problem from finance.
