  The classical Method of Successive Approximations (MSA) is an iterative
method for solving stochastic control problems and is derived from Pontryagin's
optimality principle. It is known that the MSA may fail to converge. Using
careful estimates for the backward stochastic differential equation (BSDE) this
paper suggests a modification to the MSA algorithm. This modified MSA is shown
to converge for general stochastic control problems with control in both the
drift and diffusion coefficients. Under some additional assumptions the rate of
convergence is shown. The results are valid without restrictions on the time
horizon of the control problem, in contrast to iterative methods based on the
theory of forward-backward stochastic differential equations.
