Numerical methods which have been developed to solve optimal feedback control problems for nonlinear, continuous-time dynamical systems, perturbed by Poisson as well as by Gaussian random white noise, are discussed. Predictor-corrector methods are modified for the nonstandard functional partial differential equation of stochastic dynamic programming to treat nonlinearities attributable to quadratic costs and nonsmoothness attributable to control switching. This numerical formulation is highly suitable for vectorization and parallelization techniques. Advanced computing techniques and hardware are used to help alleviate Bellman's curse of dimensionality in dynamic programming computations.
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