Bellman equation

A Bellman equation, named after its discoverer, Richard Bellman, also known as a dynamic programming equation, 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 simpler subproblems, as Bellman's "Principle of Optimality" prescribes.