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Differentiability of the Value Function in Continuous–Time Economic Models

  • Juan Pablo Rinc ́on–Zapatero

    ()

    (Universidad Carlos III de Madrid)

  • Manuel S. Santos

    ()

    (Department of Economics, University of Miami)

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.

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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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Paper provided by University of Miami, Department of Economics in its series Working Papers with number 2010-28.

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Date of creation: Jul 2010
Date of revision:
Publication status: Forthcoming: Under review
Handle: RePEc:mia:wpaper:2010-28
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