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

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

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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File URL: http://dx.doi.org/10.1002/oca.1011
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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. 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).
  2. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
  3. 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.
  4. R. Boucekkine & G. Fabbri & F. Gozzi, 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Post-Print hal-00743831, HAL.
  5. Fabrice Collard & Omar Licandro & Luis A. Puch, 2008. "The short-run Dynamics of Optimal Growth Model with Delays," Annals of Economics and Statistics, GENES, issue 90, pages 127-143.
  6. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 635-669, August.
  7. repec:hal:wpaper:halshs-00535592_v1 is not listed on IDEAS
  8. Bambi, Mauro & Gozzi, Fausto & Licandro, Omar, 2014. "Endogenous growth and wave-like business fluctuations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 68-111.
  9. 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.
  10. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  11. 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.
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