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The Once But Not Twice Differentiability of the Policy Function
A. Araujo
Abstract
It is shown that an increasing policy function that is the solution of a $C^2$ dynamic programming problem is always $C^1$. This implies that the value function is $C^2$. Examples are given to show that the policy function might not be twice differentiable and therefore the value might not be three times differentiable, even if the program is $C^3$.
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