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Optimal control in infinite horizon problems : a Sobolev space approach

  • Cuong Le Van

    ()

    (CERMSEM)

  • Raouf Boucekkine

    ()

    (CORE)

  • Cagri Saglam

    (Bilkent University)

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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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2005/B05094.pdf
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Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b05094.

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Length: 21 pages
Date of creation: Sep 2005
Date of revision:
Handle: RePEc:mse:wpsorb:b05094
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  1. 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.
  2. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  3. Askenazy, Philippe & Le Van, 1997. "A model of optimal growth strategy," CEPREMAP Working Papers (Couverture Orange) 9707, CEPREMAP.
  4. 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.
  5. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
  6. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
  7. 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.
  8. 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.
  9. Ngo Van Long & Koji Shimomura, 2003. "A Note on Transversality Conditions," Discussion Paper Series 144, Research Institute for Economics & Business Administration, Kobe University.
  10. Cuong Le Van, 1996. "Complete characterization of Yannelis-Zame and Chichilnisky-Kalman-Mas-Colell properness conditions on preferences for separable concave functions defined in $L^{p}_{+}.$ and Lp (*)," Economic Theory, Springer, vol. 8(1), pages 155-166.
  11. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March.
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