Smoothness of the Policy Function in Discrete Time Economic Models
证明，在目标函数二次连续可微且强凹的条件下，任何内点最优路径关于初始状态是连续可微的，为最优路径的定性分析提供了微分方法的理论基础。
The theory applying to dynamic programming has furnished a useful set of techniques for the analysis of many types of sequential models. This theory, however, has not yielded heretofore much information about the differentiability properties of optimal solutions. This aspect is of particular interest as regards the qualitative analysis of optimal paths, where differentiable methods are often called into play. This paper shows roughly that if the objective is twice continuously differentiable and strongly concave, then any interior optimal path is continuously differentiable with respect to the initial state. Copyright 1991 by The Econometric Society.