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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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Bibliographic Info

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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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 0436, Econometric Society.
  2. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
  3. Raouf BOUCEKKINE & Giorgio FABBRI & Fausto GOZZI, 2009. "Maintenance and investment : Complements or Substitutes ? A Reappraisal," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2009010, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  4. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00827641, HAL.
  5. 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.
  6. Luis A. Puch & Fabrice Collard & Omar Licandro, 2004. "The short-run dynamics of optimal growth models with delays," Computing in Economics and Finance 2004 117, Society for Computational Economics.
  7. 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.
  8. 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.
  9. Mauro Bambi & Omar Licandro, 2011. "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona Graduate School of Economics.
  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," Computing in Economics and Finance 2006 77, Society for Computational Economics.
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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, 2013. "Short-Run Pain, Long-Run Gain: The Conditional Welfare Gains from International Financial Integration," Working Papers halshs-00790569, HAL.
  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.

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