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On High-Order Differentiability of the Policy Function

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  • Santos, Manuel S

Abstract

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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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 3 (1993)
Issue (Month): 3 (July)
Pages: 565-70

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Handle: RePEc:spr:joecth:v:3:y:1993:i:3:p:565-70

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Web page: http://link.springer.de/link/service/journals/00199/index.htm

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Cited by:
  1. Bona, Jerry L. & Santos, Manuel S., 1997. "On the Role of Computation in Economic Theory," Journal of Economic Theory, Elsevier, vol. 72(2), pages 241-281, February.
  2. Noah Williams, 2003. "Small Noise Asymptotics for a Stochastic Growth Model," Computing in Economics and Finance 2003 262, Society for Computational Economics.
  3. Jesús Antón & Emilio Cerdá & Elena Huergo, 1998. "Sensitivity analysis in A class of dynamic optimization models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 6(1), pages 97-121, June.
  4. Montrucchio, Luigi, 1998. "Thompson metric, contraction property and differentiability of policy functions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 449-466, January.
  5. Joël Blot & Bertrand Crettez, 2004. "On the smoothness of optimal paths," Decisions in Economics and Finance, Springer, vol. 27(1), pages 1-34, 08.
  6. Chen, Yu & Cosimano, Thomas F. & Himonas, Alex A., 2008. "Analytic solving of asset pricing models: The by force of habit case," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3631-3660, November.
  7. Yu Chen & Thomas Cosimano & Alex Himonas, 2010. "Continuous time one-dimensional asset-pricing models with analytic price–dividend functions," Economic Theory, Springer, vol. 42(3), pages 461-503, March.

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