In the long history of mathematics, stochastic optimal control is a rather recent development. Using Bellman’s Principle of Optimality along with measure-theoretic and functional-analytic methods, several mathematicians such as H. Kushner, W. Fleming, R. Rishel. W.M. Wonham and J.M. Bismut, among many others, made important contributions to this new area of mathematical research during the 1960s and early 1970s. For a complete mathematical exposition of the continuous time case see Fleming and Rishel (1975) and for the discrete time case see Bertsekas and Shreve (1978).