A characterization for solutions of stochastic discrete time optimization models

A notion of finitely optimal plan for intertemporal optimization problems as a necessary condition for optimality is introduced. Under interiority of a feasible plan and differentiability of the return function, such a plan satisfies the stochastic analogue of deterministic Euler-Lagrange conditions, which become also sufficient conditions under concavity of the return function. Then, under more general assumptions, a sufficient criterion of optimality based on competitive plans supported by price systems and transversality conditions is discussed. Differently from the current literature, no restrictive hypotheses on the probability measure of the random shocks are assumed.