动态不一致Bellman方程的一些数学性质——关于双边利他主义动力学的注解

Takaaki Aoki
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摘要

本文描述了将双边利他主义与OLG设置结合在一起的动态效用的一些动态方面。我们分析了双边利他主义权值动态不一致的特殊情况。证明了双边利他主义的Bellman方程可以简化为单侧动态问题,但其有效折现因子仅在当代是不同的。我们证明了值函数的收缩映射结果在一般情况下是不能实现的,并且局部可以存在无穷多个具有不同稳态的自洽策略函数(自洽策略函数的不确定性)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics
This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. We analyzed the special case where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. We show that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions with distinct steady states (indeterminacy of self-consistent policy functions).
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