Econometrica: Sep 1991, Volume 59, Issue 5

The Once But Not Twice Differentiability of the Policy Function<1383:TOBNTD>2.0.CO;2-A
p. 1383-1393

A. Araujo

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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