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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 Paris I - Panthéon-Sorbonne, CORE - Center of Operation Research and Econometrics [Louvain] - Université Catholique de Louvain (UCL) - Belgique)

  • Raouf Boucekkine

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

  • Cagri Saglam

    (Bilkent - University of Turkey)

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.

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

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

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  1. 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.
  2. Ngo Van Long & Koji Shimomura, 2003. "A Note on Transversality Conditions," Discussion Paper Series, Research Institute for Economics & Business Administration, Kobe University 144, Research Institute for Economics & Business Administration, Kobe University.
  3. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, Elsevier, vol. 27(1), pages 1-19, June.
  4. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 8024, Universite de Montreal, Departement de sciences economiques.
  5. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, Elsevier, vol. 85(1), pages 24-51, March.
  6. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, Econometric Society, vol. 42(2), pages 267-72, March.
  7. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, Elsevier, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
  8. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, Econometric Society, vol. 69(4), pages 995-1012, July.
  9. 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, Springer, vol. 8(1), pages 155-166.
  10. Araujo,A. & Monteiro,P.K., 1989. "General equilibrium with infinitely many goods: The case of seperable utilities," Discussion Paper Serie A, University of Bonn, Germany 249, University of Bonn, Germany.
  11. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
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Cited by:
  1. Erol Dogan & Cuong Le Van & Cagri Saglam, 2010. "Optimal timing of regime switching in optimal growth models: A Sobolev space approach," Working Papers 16, Development and Policies Research Center (DEPOCEN), Vietnam.
  2. Aditya Goenkay & Lin Liu & Manh-Hung Nguyen, 2013. "Infectious Diseases and Economic Growth," Working Papers 06, Development and Policies Research Center (DEPOCEN), Vietnam.
  3. 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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