On the smoothness of optimal paths

The aim of this paper is to study the differentiability property of optimal paths in dynamic economic models. We address this problem from the point of view of the differential calculus in sequence spaces which are infinite-dimensional Banach spaces. We assume that the return or utility function is...

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Vydáno v:Decisions in economics and finance Ročník 27; číslo 1; s. 1 - 34
Hlavní autoři: Blot, Joël, Crettez, Bertrand
Médium: Journal Article
Jazyk:angličtina
Vydáno: Milano Springer 01.08.2004
Springer Nature B.V
Edice:Decisions in Economics and Finance
Témata:
Banach spaces
Capital
Capital stock
Discount rates
Economic models
Eigenvalues
Function
Growth models
Point of view
Property
Studies
Toll roads
Utility functions
ISSN:1593-8883, 1129-6569
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Shrnutí:The aim of this paper is to study the differentiability property of optimal paths in dynamic economic models. We address this problem from the point of view of the differential calculus in sequence spaces which are infinite-dimensional Banach spaces. We assume that the return or utility function is concave, and that optimal paths are interior and bounded. We study the The aim of this paper is to study the differentiability property of optimal paths in dynamic economic models. We address this problem from the point of view of the differential calculus in sequence spaces which are infinite-dimensional Banach spaces. We assume that the return or utility function is concave, and that optimal paths are interior and bounded. We study the <C<<<r< differentiability of optimal paths vis-a-vis different parameters. These parameters are: the initial vector of capital stock, the discount rate and a parameter which lies in a Banach space (which could be the utility function itself). The method consists of applying an implicit function theorem on the Euler-Lagrange equation. In order to do this, we make use of classical conditions (i.e., the dominant diagonal block assumption) and we provide new ones. [PUBLICATION ABSTRACT]
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ISSN:1593-8883
1129-6569
DOI:10.1007/s10203-004-0042-5