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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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Suggested Citation

  • BOUCEKKINE, Raouf & FABBRI, Giorgio & PINTUS, Patrick, 2012. "On the optimal control of a linear neutral differential equation arising in economics," CORE Discussion Papers RP 2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:2449
    Note: In : Optimal Control Applications and Methods, 33(5), 511-530, 2012
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    File URL: http://dx.doi.org/10.1002/oca.1011
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    1. 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.
    2. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    3. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    4. 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.
    5. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
    6. 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.
    7. 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.
    8. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 635-669, August.
    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.
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    Cited by:

    1. Raouf Boucekkine & Giorgio Fabbri & Patrick A. Pintus, 2018. "Short-run pain, long-run gain: the conditional welfare gains from international financial integration," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 329-360, March.
    2. Javier de Frutos & Guiomar Martín-Herrán, 2016. "Pollution control in a multiregional setting: a differential game with spatially distributed controls," Gecomplexity Discussion Paper Series 201601, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2016.
    3. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Bounded interest rate feedback rules in continuous-time," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 227-236.
    4. Fabbri, Giorgio, 2017. "International borrowing without commitment and informational lags: Choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 103-114.
    5. 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 27 Jun 2016.

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