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Optimal control in infinite horizon problems : a Sobolev space approach

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  • Cuong Le Van

    ()
    (CERMSEM)

  • Raouf Boucekkine

    ()
    (CORE)

  • Cagri Saglam

    (Bilkent University)

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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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2005/B05094.pdf
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Bibliographic Info

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

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References

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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 144, Research Institute for Economics & Business Administration, Kobe University.
  3. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
  4. 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.
  5. 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.
  6. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-85, July.
  7. 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.
  8. Askenazy, Philippe & Le Van, 1997. "A model of optimal growth strategy," CEPREMAP Working Papers (Couverture Orange) 9707, CEPREMAP.
  9. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  10. 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.
  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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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. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
  3. Yoichi Otsubo & Theoharry Grammatikos & Thorsten Lehnert, 2012. "Market Perceptions of US and European Policy Actions Around the Subprime Crisis," CREA Discussion Paper Series 12-14, Center for Research in Economic Analysis, University of Luxembourg.

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