The Once But Not Twice Differentiability of the Policy Function - Araujo, A. (Econometrica, 1991)
It is shown that an increasing policy function that is the solution of a C(superscript "2") dynamic programming problem is always C(superscript "1"). This implies that the value function is C(superscript "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(superscript "3"). Copyright 1991 by The Econometric Society.