Summary
This note presents some results concerning high-order differentiability of the policy function. It is shown that simple examples of cubic return functions may yield optimal policies which under standard conditions are not differentiable to high order. The loss of differentiability, however, is not robust to small perturbations of the model. For instance, monotone policy functions are almost always high-order differentiable.
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Santos, M.S. On high-order differentiability of the policy function. Econ Theory 3, 565–570 (1993). https://doi.org/10.1007/BF01209702
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DOI: https://doi.org/10.1007/BF01209702