Econ Papers Daily / 期刊论文
论递归效用的存在性
On the existence of recursive utility
摘要
Recursive utility functions are often defined implicitly, as the solution of a functional equation known as the Koopmans recursion. As conditions for a unique solution can be demanding, and uniqueness itself has proven restrictive in some applications, I investigate the existence of a least and greatest solution, both of which possess a number of attractive properties. While a least solution can be shown to exist in great generality, I show that a greatest solution need not. I then identify a sufficient condition for the existence of a greatest solution, which imposes a minimal form of discounting on preferences. The condition is shown to be necessary whenever the greatest solution is computable by standard iterative methods.
中文摘要
递归效用函数通常以隐式方式定义，即作为被称为Koopmans递归的函数方程的解。由于唯一解的条件可能相当苛刻，且唯一性本身在一些应用中已被证明具有限制性，我考察了最小解与最大解的存在性，二者均具有若干吸引人的性质。尽管最小解可在相当一般的条件下被证明存在，但我表明最大解未必存在。随后，我识别出最大解存在的一个充分条件，该条件对偏好施加了一种最低形式的贴现。当最大解可通过标准迭代方法计算时，该条件被证明是必要的。