Viscosity solutions approach to economic models governed by DDEs
Giorgio Fabbri ()
MPRA Paper from University Library of Munich, Germany
A family of economic and demographic models governed by linear delay differential equations is considered. They can be expressed as optimal control problems subject to delay differential equations (DDEs) characterized by some non-trivial mathematical difficulties: state/control constraints and delay in the control. The study is carried out rewriting the problem as an (equivalent) optimal control problem in infinite dimensions and then using the dynamic programming approach (DPA). Similar problems have been studied in the literature using classical and strong (approximating) solutions of the Hamilton-Jacobi-Bellman (HJB) equation. Here a more general formulation is treated thanks to the use of viscosity solutions approach. Indeed a general current objective function is considered and the concavity of the Hamiltonian is not required. It is shown that the value function is a viscosity solution of the HJB equation and a verification theorem in the framework of viscosity solutions is proved.
Keywords: viscosity solutions; delay differential equation; vintage models (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (1) Track citations by RSS feed
Downloads: (external link)
https://mpra.ub.uni-muenchen.de/2826/1/MPRA_paper_2826.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/5117/1/MPRA_paper_5117.pdf revised version (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:2826
Access Statistics for this paper
More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Series data maintained by Joachim Winter ().