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On the optimal control of a linear neutral differential equation arising in economics

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  • Raouf Boucekkine

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

  • Giorgio Fabbri

    ()
    (Dipartimento Matematica e statistica - Université de Naples)

  • Patrick-Antoine Pintus

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

Abstract

In this paper, we apply two optimization methods to solve an optimal control problem of a linear neutral differential equation (NDE) arising in economics. The first one is a variational method, the second follows a dynamic programming approach. Due to the infinite dimensionality of the NDE, the second method requires the reformulation of the latter as an ordinary differential equation in an appropriate abstract space. It is shown that the resulting HJB equation admits a closed-form solution, allowing for a much finer characterization of the optimal dynamics compared to the alternative variational method. The latter is clearly limited by the nontrivial nature of asymptotic analysis of NDEs.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00576770.

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Date of creation: 15 Mar 2011
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Handle: RePEc:hal:wpaper:halshs-00576770

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Related research

Keywords: Neutral differential equations; economic dynamics; optimal control; calculus of variations; dynamic programming; infinite dimension;

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References

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  1. R. Boucekkine & F. del Rio & O. Licandro & Luis A. Puch, 2000. "Vintage Capital and the Dynamics of the AK Model," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 0436, Econometric Society.
  2. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, Elsevier, vol. 74(2), pages 333-348, June.
  3. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2009. "Maintenance and investment: complements or substitutes? A reappraisal," Working Papers, Business School - Economics, University of Glasgow 2009_21, Business School - Economics, University of Glasgow.
  4. Fabrice Collard & Omar Licandro & Luis A. Puch, . "The short-run dynamics of optimal growth models with delays," Working Papers 2004-05, FEDEA.
  5. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Documents de recherche, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne 13-09, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
  6. Raouf Boucekkine & Marc Germain & Omar Licandro, . "Replacement echoes in the vintage capital growth model," Working Papers 96-16, FEDEA.
  7. Fabrice Collard & Omar Licandro & Luis A. Puch, 2003. "The short-run dynamics of optimal growth models with delays," Documentos de Trabajo del ICAE, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico 0311, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  8. Raouf Boucekkine & Patrick-Antoine Pintus, 2010. "Is History a Blessing or a Curse? International Borrowing without Commitment, Leapfrogging and Growth Reversals," Working Papers halshs-00535592, HAL.
  9. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer, Springer, vol. 50(3), pages 635-669, August.
  10. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, Elsevier, vol. 143(1), pages 331-373, November.
  11. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers, European University Institute ECO2006/17, European University Institute.
  12. repec:hal:wpaper:halshs-00535592_v1 is not listed on IDEAS
  13. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, . "Vintage capital and the dynamics of the AK model," Working Papers 2000-01, FEDEA.
  14. Mauro Bambi & Omar Licandro, 2011. "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona Graduate School of Economics.
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Citations

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Cited by:
  1. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2013. "Bounded Interest Rate Feedback Rules in Continuous-Time," MPRA Paper 45424, University Library of Munich, Germany.
  2. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," DEOS Working Papers 1402, Athens University of Economics and Business.
  3. Raouf Boucekkine & Giorgio Fabbri & Patrick A. Pintus, 2014. "Short-Run Pain, Long-Run Gain: The Conditional Welfare Gains from International Financial Integration," Working Papers halshs-00790569, HAL.
  4. Raouf Boucekkine & Giorgio Fabbri & Patrick Pintus, 2012. "Short-Run Pain, Long-Run Gain: The Conditional Welfare Gains from International Financial Integration The Conditional Welfare Gains from International Financial Integration," AMSE Working Papers 1202, Aix-Marseille School of Economics, Marseille, France, revised 12 Sep 2014.

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