On the optimal control of some parabolic partial differential equations arising in economics
We review an emerging application field to parabolic partial differential equa- tions (PDEs), that’s economic growth theory. After a short presentation of con- crete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular, the heuristic appli- cation of the maximum principle to the latter leads to single out a serious ill- posedness problem, which is, in our view, a barrier to the use of parabolic PDEs in economic growth studies as the latter are interested in long-run asymptotic solu- tions, thus requiring the solution to infinite time horizon optimal control problems. Adapted dynamic programming methods are used to dig deeper into the identified ill-posedness issue.
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2010_06, Business School - Economics, University of Glasgow.
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- 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.
- Raouf BOUCEKKINE & Carmen CAMACHO & Giorgio FABBRI, 2010. "Spatial dynamics and convergence: the spatial AK model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2010009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Documents de recherche 13-09, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
- Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00827641, HAL.
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