On a class of dynamic programming problems whose optimal controls and states are independent of the future

When applying dynamic programming for optimal decision making one usually needs considerable knowledge about the future. This knowledge, e.g. about future functions and parameters, necessary to determine optimal control policies, however, is often not available and thus precludes the application of dynamic programming.In the present paper it is shown that for a certain class of dynamic programming problems the optimal control policy is independent of the future. To illustrate the results an application in inventory control is given and further applications in the theories of economic growth and corporate finance are listed in the references.