Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence
提出双收敛概念，一种关于效用函数和生产函数的弱拓扑假设，证明在此假设下递归效用函数是Koopmans方程的唯一可容许解，动态规划中的真实值函数是Bellman方程的唯一可容许解，并可通过逐次逼近计算。
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.