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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. Raouf Boucekkine & Marc Germain & Omar Licandro, . "Replacement echoes in the vintage capital growth model," Working Papers 96-16, FEDEA.
  2. 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.
  3. Collard, Fabrice & Licandro, Omar & Puch, Luis, 2005. "The Short-Run Dynamics of Optimal Growth Models with Delays," CEPR Discussion Papers 5414, C.E.P.R. Discussion Papers.
  4. 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).
  5. Bambi, Mauro & Fabbri, Giorgio & Gozzi, Fausto, 2009. "Optimal policy and consumption smoothing effects in the time-to-build AK model," MPRA Paper 17128, University Library of Munich, Germany.
  6. 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.
  7. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Documents de travail du Centre d'Economie de la Sorbonne 13047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  8. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2009. "Maintenance and investment: complements or substitutes? A reappraisal," Working Papers 2009_21, Business School - Economics, University of Glasgow.
  9. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  10. repec:hal:wpaper:halshs-00535592_v1 is not listed on IDEAS
  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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