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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.

Suggested Citation

  • Santos, Manuel S, 1993. "On High-Order Differentiability of the Policy Function," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(3), pages 565-570, July.
  • Handle: RePEc:spr:joecth:v:3:y:1993:i:3:p:565-70
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    1. repec:eee:macchp:v2-527 is not listed on IDEAS
    2. 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.
    3. Joël Blot & Bertrand Crettez, 2004. "On the smoothness of optimal paths," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 1-34, August.
    4. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, Elsevier.
    5. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2014. "Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty," Computational Optimization and Applications, Springer, vol. 58(1), pages 31-85, May.
    6. Yu Chen & Thomas Cosimano & Alex Himonas, 2010. "Continuous time one-dimensional asset-pricing models with analytic price–dividend functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 461-503, March.
    7. 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.
    8. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
    9. 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;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 97-121, June.
    10. 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.

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