Necessary and Sufficient Conditions for a Solution of the Bellman Equation to be the Value Function: A General Principle

In this paper, we give Necessary and Sufficient Conditions for a Solution of the Belman Equation to be the Value Function. This result is a general principle. It requires no structure beyond the common framework of discrete-time stationary optimization problems with time-additive returns. In particular, the state space X is an arbitrary set.