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Optimal control in infinite horizon problems : a Sobolev space approach

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Cuong Le Van () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I, CORE - Université Catholique de Louvain)
Raouf Boucekkine () (CORE - Université Catholique de Louvain)
Cagri Saglam (Bilkent - University of Turkey)

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Abstract

In this paper, we make use of the Sobolev space W1,1(R+, Rn) to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L1 spaces have natural positive cones with no interior points.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00197546_v1.

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Date of creation: Sep 2005
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Handle: RePEc:hal:cesptp:halshs-00197546_v1

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Related research
Keywords: Optimal control; Sobolev spaces; transversality conditions; order ideal.;

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  1. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June. [Downloadable!] (restricted)
  2. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, vol. 85(1), pages 24-51, March. [Downloadable!] (restricted)
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  3. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  4. Ngo Van Long & Koji Shimomura, 2003. "A Note on Transversality Conditions," Discussion Paper Series 144, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
  5. Bonnisseau, Jean-Marc & Le Van, Cuong, 1996. "On the subdifferential of the value function in economic optimization problems," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 55-73. [Downloadable!] (restricted)
  6. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier. [Downloadable!] (restricted)
  7. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany. [Downloadable!]
  8. Araujo,A. & Monteiro,P.K., 1989. "General equilibrium with infinitely many goods: The case of seperable utilities," Discussion Paper Serie A 249, University of Bonn, Germany.
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