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 interioiity 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 Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1022.
Date of creation: Sep 2010
Date of revision:
Constrained optimization; Value function; Differentiability; Envelope theorem; Duality theory;
Other versions of this item:
- 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.
- 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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