A **Bellman equation**, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming.

It writes the “value” of a decision problem at a certain point in time in terms of the payoff from some initial choices and the “value” of the remaining decision problem that results from those initial choices.

This breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman’s “principle of optimality” prescribes.