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

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  • BOUCEKKINE, Raouf
  • FABBRI, Giorgio
  • PINTUS, Patrick

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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -2449.

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Handle: RePEc:cor:louvrp:-2449

Note: In : Optimal Control Applications and Methods, 33(5), 511-530, 2012
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  1. Raouf BOUCEKKINE & Carmen CAMACHO & Giorgio FABBRI, 2010. "Spatial dynamics and convergence: the spatial AK model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2010009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  2. Raouf BOUCEKKINE & Patrick A. PINTUS, 2010. "Is History a Blessing or a Curse? International Borrowing without Commitment, Leapfrogging and Growth Reversals," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2010038, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  3. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer, vol. 50(3), pages 635-669, August.
  4. Boucekkine, R. & Germain, M. & Licandro, O., . "Replacement echoes in the vintage capital growth model," CORE Discussion Papers RP -1275, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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 0436, Econometric Society.
  6. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
  7. Fabrice Collard & Omar Licandro & Luis A. Puch, . "The short-run dynamics of optimal growth models with delays," Working Papers 2004-05, FEDEA.
  8. Mauro Bambi & Omar Licandro, 2011. "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona Graduate School of Economics.
  9. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
  10. 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.
  11. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
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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. Raouf Boucekkine & Giorgio Fabbri & Patrick A. Pintus, 2012. "Short-Run Pain, Long-Run Gain : the Conditional Welfare Gains from International Financial Integration," Documents de recherche 12-14, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
  3. 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 Feb 2012.
  4. 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.

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