Summary. In this paper it is demonstrated how necessary and sufficient conditions for optimality of a strategy in multi-stage stochastic programs may be obtained without topological assumptions. The conditions are essentially based on a dynamic programming approach. These conditions - called conserving and equalizing - show the essential difference between finite-stage and infinite-stage stochastic programs.
Moreover, it is demonstrated how a recursive structure of the problem can give a reformulation of the conditions. These reformulated conditions may be used for the construction of numerical solution techniques.