Differentiability of the Value Function in Continuous–Time Economic Models
AbstractIn 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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Bibliographic InfoPaper provided by University of Miami, Department of Economics in its series Working Papers with number 2010-28.
Date of creation: Jul 2010
Date of revision:
Publication status: Forthcoming: Under review
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Constrained optimization; value function; differentiability; envelope therem; duality theory.;
Other versions of this item:
- Juan Pablo Rincón-Zapatero & Manuel S. Santos, 2010. "Differentiability of the value function in continuous-time economic models," Economics Working Papers we1022, Universidad Carlos III, Departamento de Economía.
- 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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- Bruno Strulovici & Martin Szydlowski, 2012.
"On the Smoothness of Value Functions,"
1542, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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