Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case
研究无界回报下贝尔曼方程解的存在唯一性，提出基于连续函数空间度量和度量不动点定理的新方法，证明解的唯一性及存在性的充分条件，并说明不动点即为值函数且可通过迭代逼近。
We study the problem of the existence and uniqueness of solutions to the Bellman equation in the presence of unbounded returns. We introduce a new approach based both on consideration of a metric on the space of all continuous functions over the state space, and on the application of some metric fixed point theorems. With appropriate conditions we prove uniqueness of solutions with respect to the whole space of continuous functions. Furthermore, the paper provides new sufficient conditions for the existence of solutions that can be applied to fairly general models. It is also proven that the fixed point coincides with the value function and that it can be approached by successive iterations of the Bellman operator.