High Quality Content by WIKIPEDIA articles! A Bellman equation (also known as a dynamic programming equation), named after its discoverer, Richard Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It breaks a dynamic optimization problem into simpler subproblems, writing 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, as Bellman's Principle of Optimality prescribes. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory.

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