Equilibrium Points for Optimal Investment with Vintage Capital
AbstractThe paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the general case are given and later applied to the economic problem of optimal investment with vintage capital. Explicit computation of equilibria for the economic problem in some relevant examples is also provided. Indeed the challenging issue here is showing that a theoretical machinery, such as optimal control in infinite dimension, may be effectively used to compute solutions explicitly and easily, and that the same computation may be straightforwardly repeated in examples yielding the same abstract structure. No stability result is instead provided: the work here contained has to be considered as a first step in the direction of studying the behavior of optimal controls and trajectories in the long run.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 182.
Length: 19 pages
Date of creation: Nov 2008
Date of revision:
Linear convex control; Boundary control; Hamilton–Jacobi–Bellman equations; Optimal investment problems; Vintage capital;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Capital; Investment; Capacity
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-12-01 (All new papers)
- NEP-BEC-2008-12-01 (Business Economics)
- NEP-MAC-2008-12-01 (Macroeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Veliov, V., 2001.
"Dynamic Investment Behavior Taking into Account Ageing of the Capital Good,"
2001-13, Tilburg University, Center for Economic Research.
- Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Veliov, V., 2004. "Dynamic investment behavior taking into account ageing of the capital good," Open Access publications from Tilburg University urn:nbn:nl:ui:12-140939, Tilburg University.
- Silvia Faggian & Fausto Gozzi, 2004. "On The Dynamic Programming Approach For Optimal Control Problems Of Pde'S With Age Structure," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 233-270.
- Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
- Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, .
"Vintage capital and the dynamics of the AK model,"
- BOUCEKKINE, Raouf & LICANDRO, Omar & PUCH, Luis A. & DEL RIO, Fernando, . "Vintage capital and the dynamics of the AK model," CORE Discussion Papers RP -1757, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- R. Boucekkine & F. del Rio & O. Licandro & Luis A. Puch, 2000. "Vintage Capital and the Dynamics of the AK Model," Econometric Society World Congress 2000 Contributed Papers 0436, Econometric Society.
- Boucekkine, Raouf & Del Rio, Fernando & Licandro, Omar, 2000. "Vintage capital and the dynamics of the AK model," CEPREMAP Working Papers (Couverture Orange) 0003, CEPREMAP.
- Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, 2003. "Vintage capital and the dynamics of the AK model," Documentos de Trabajo del ICAE 0310, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
- Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 1999. "Vintage Capital and the Dynamics of the AK Model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Raouf BOUCEKKINE & Omar LICANDRO & Luis A. PUCH & Fernando DEL RIO, 2002. "Vintage Capital And the Dynamics of the AK Model," Economics Working Papers ECO2002/07, European University Institute.
- Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
- Fabbri, Giorgio & Gozzi, Fausto, 2006. "Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version," MPRA Paper 7334, University Library of Munich, Germany.
- Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006.
"Anticipation effects of technological progress on capital accumulation: a vintage capital approach,"
Journal of Economic Theory,
Elsevier, vol. 126(1), pages 143-164, January.
- Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Veliov, V.M., 2005. "Anticipation effects of technological progress on capital accumulation : a vintage capital approach," Open Access publications from Tilburg University urn:nbn:nl:ui:12-148454, Tilburg University.
- Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
- Faggian, Silvia & Gozzi, Fausto, 2010.
"Optimal investment models with vintage capital: Dynamic programming approach,"
Journal of Mathematical Economics,
Elsevier, vol. 46(4), pages 416-437, July.
- Silvia Faggian & Fausto Gozzi, 2008. "Optimal investment models with vintage capital: Dynamic Programming approach," Working Papers 174, Department of Applied Mathematics, Università Ca' Foscari Venezia.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marco LiCalzi).
If references are entirely missing, you can add them using this form.