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Optimal control in infinite horizon problems: a Sobolev spaces approach

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  • Cuong Le Van

    () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Raouf Boucekkine

    (CORE - Center of Operation Research and Econometrics [Louvain] - Université Catholique de Louvain (UCL) - Belgique)

  • Cagri Saglam

    (Universite Bilkent [Ankara] - Universite Bilkent)

Abstract

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

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00101140.

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Date of creation: Sep 2007
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Publication status: Published, Economic Theory, 2007, 32, 3, 497-509
Handle: RePEc:hal:cesptp:halshs-00101140

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00101140
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Keywords: Optimal control; Sobolev spaces; Transversality conditions; Order ideal;

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  1. Askenazy, P. & Le Van, C., 1997. "A Model of Optimal Growth Strategy," DELTA Working Papers 97-27, DELTA (Ecole normale supérieure).
  2. 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.
  3. 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.
  4. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
  5. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
  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.
  7. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  8. Ngo Van Long & Koji Shimomura, 2003. "A Note on Transversality Conditions," Discussion Paper Series 144, Research Institute for Economics & Business Administration, Kobe University.
  9. 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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Cited by:
  1. Cuong Le Van & Erol Dogan & Cagri Saglam, 2011. "Optimal timing of regime switching in optimal growth models: A Sobolev space approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00549165, HAL.
  2. Patrice Pieretti & Skerdilajda Zanaj & Benteng Zou, 2012. "On the long run economic performance of small economies," CREA Discussion Paper Series 12-14, Center for Research in Economic Analysis, University of Luxembourg.

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