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On the optimal control of a linear neutral differential equation arising in economics
Author(s) -
Boucekkine Raouf,
Fabbri Giorgio,
Pintus Patrick
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.1011
Subject(s) - curse of dimensionality , optimal control , mathematics , ordinary differential equation , differential equation , space (punctuation) , dynamic programming , differential (mechanical device) , mathematical analysis , mathematical optimization , computer science , physics , statistics , operating system , thermodynamics
SUMMARY 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. Copyright © 2011 John Wiley & Sons, Ltd.