Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence

Abstract

This paper introduces the concept of biconvergence, which is a weak and intuitive topological assumption on the utility function and the production function together. Concerning recursive utility, the author shows that, given biconvergence, the utility function is the unique admissible solution to Koopman's equation. Concerning dynamic programming, he shows that, given biconvergence, the true value function exists, it is the unique admissible solution to Bellman's equation, and it may be calculated numerically as the limit of successive approximations. Finally, he develops an overly strong sufficient condition for biconvergence that substantially weakens the Lipschitz condition used by contraction-mapping techniques. Copyright 1990 by The Review of Economic Studies Limited.