This paper deals with the nite horizon stochastic optimal control problem with the expectation of the p-norm as the objective function and jointly Gaussian, although not necessarily independent, additive disturbance process. We develop an approximation strategy that solves the problem in a certain class of nonlinear feedback policies while ensuring satisfaction of hard input constraints. A bound on suboptimality of the proposed strategy in this class of nonlinear feedback policies is given for the special case of p = 1. We also develop a recursively feasible receding horizon policy with respect to state chance constraints and/or hard control input constraints in the presence of bounded disturbances. The performance of the proposed policies is examined in two numerical examples.