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

Boucekkine, Raouf;Fabbri, Giorgio;Pintus, Patrick
(2012) Optimal Control Applications and Methods — Vol. 33, n° 5, p. 511-530 (2012)

Files

Rep2449.pdf
  • Closed Access
  • Adobe PDF
  • 343.77 KB
Request a copy

Details

Authors
  • Boucekkine, RaoufUCLouvain
    Author
  • Fabbri, GiorgioUniversita di Napoli Parthenope, Naples, Italy
    Author
  • Pintus, PatrickUniversité Aix-Marseille and GREQAM-IDEP, Marseille, France
    Author
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, and the second follows a dynamic programming approach. Because of 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 Hamilton–Jacobi–Bellman equation admits a closed-form solution, allowing for a much finer characterization of the optimal dynamics compared with the alternative variational method. The latter is clearly limited by the nontrivial nature of asymptotic analysis of NDEs.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Boucekkine, R., Fabbri, G., & Pintus, P. (2012). On the optimal control of a linear neutral differential equation arising in economics. Optimal Control Applications and Methods, 33(5), 511-530. https://doi.org/10.1002/oca.1011 (Original work published 2012)