Iterative algorithms for solving undiscounted bellman equations

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Abstract
A new class of iterative algorithms for solving undiscounted Bellman equations is proposed in this article, Such algorithms are proved to be particularly useful in handling “degenerate” equations. For simplicity of presentation and for motivation of basic ideas, the algorithms are introduced in terms of three control problems, one optimal stopping time problem and two singular stochastic control problems. The convergence and rates of convergence are obtained. These results are based on the introduction of a performance index of approximation, which makes new algorithms differ from the existing ones for solving regular undiscounted Bellman equations in the control literature.