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Differentiability of the Value Function in Continuous–Time Economic Models

Author

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  • Juan Pablo Rinc ́on–Zapatero

    () (Universidad Carlos III de Madrid)

  • Manuel S. Santos

    () (Department of Economics, University of Miami)

Abstract

In this paper we provide some sufficient conditions for the differentiability of the value function in a class of infinite-horizon continuous-time models of convex optimization arising in economics. We dispense with an interiority condition which is quite restrictive in constrained optimization and it is usually hard to check in applications. The differentiability of the value function is used to prove Bellman’s equation as well as the existence and continuity of the optimal feedback policy. We also establish uniqueness of the vector of dual variables under some conditions that rule out existence of asset pricing bubbles.

Suggested Citation

  • Juan Pablo Rinc ́on–Zapatero & Manuel S. Santos, 2010. "Differentiability of the Value Function in Continuous–Time Economic Models," Working Papers 2010-28, University of Miami, Department of Economics.
  • Handle: RePEc:mia:wpaper:2010-28
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    File URL: http://www.bus.miami.edu/_assets/files/faculty-and-research/academic-departments/eco/eco-working-papers/2010/wp-2010-28-Cont_Time_Julio_2010.pdf
    File Function: First version, 2010
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    Cited by:

    1. Bruno Strulovici & Martin Szydlowski, 2012. "On the Smoothness of Value Functions," Discussion Papers 1542, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Strulovici, Bruno & Szydlowski, Martin, 2015. "On the smoothness of value functions and the existence of optimal strategies in diffusion models," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 1016-1055.

    More about this item

    Keywords

    Constrained optimization; value function; differentiability; envelope therem; duality theory.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)

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