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

Author

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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," LIDAM Reprints CORE 2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2449
    DOI: 10.1002/oca.1011
    Note: In : Optimal Control Applications and Methods, 33(5), 511-530, 2012
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    Cited by:

    1. Fabbri, Giorgio, 2017. "International borrowing without commitment and informational lags: Choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 103-114.
    2. 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.
    3. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games," European Journal of Operational Research, Elsevier, vol. 276(1), pages 379-394.
    4. Carmen Camacho & Agustín Pérez-Barahona, 2017. "The diffusion of economic activity across space: a new approach," Working Papers halshs-01670532, HAL.
    5. 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.
    6. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    7. 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.
    8. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    9. 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.
    10. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.

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