STATIONARY RECURSIVE UTILITY AND DYNAMIC-PROGRAMMING UNDER THE ASSUMPTION OF BICONVERGENCE

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, we show that, given biconvergence, the utility function is the unique admissible solution to Koopmans' equation. Concerning dynamic programming, we show 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, we develop an overly strong sufficient condition for biconvergence which substantially weakens the Lipschitz condition used by contraction-mapping techniques. © 1990 The Review of Economic Studies Limited.