Do not Blame Bellman: It Is Koopmans' Fault
基于塔斯基不动点定理，为递归效用的随机动态规划提供统一方法，指出多重值源于多个递归效用，并论证贝尔曼算子的最大不动点应具有特权地位。
We provide a unified approach to stochastic dynamic programming with recursive utility based on an elementary application of Tarski's fixed point theorem. We establish that the exclusive source of multiple values is the presence of multiple recursive utilities consistent with the given aggregator, each yielding a legitimate value of the recursive program. We also present sufficient conditions ensuring a unique value of the recursive program in some circumstances. Overall, acknowledging the unavoidable failure of uniqueness in general, we argue that the greatest fixed point of the Bellman operator should have a privileged position.