In this paper, a new method of solving stochastic optimization problems is presented. Specifically, the stochastic problem statement is reformulated as a deterministic one to which well-known methods (i.e. the calculus of variations and the maximum principle) can be applied. The procedure by which this is achieved involves the conditional probability density function of the process; the density function is expanded in an infinite series and conditions necessary for this series to satisfy the Fokker-Planck equation are obtained. These conditions, which are differential constraints on the coefficients of the series, constitute an infinite set of deterministic state equations.