Optimal investment models with vintage capital: Dynamic programming approach
The dynamic programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers ([Barucci and Gozzi, 1998], [Barucci and Gozzi, 2001], [Feichtinger et al., 2003] and [Feichtinger et al., 2006]) either in cases when explicit solutions can be found or using Maximum Principle techniques. The problem is rephrased into an infinite dimensional setting, it is proven that the value function is the unique regular solution of the associated stationary Hamilton-Jacobi-Bellman equation, and existence and uniqueness of optimal feedback controls is derived. It is then shown that the optimal path is the solution to the closed loop equation. Similar results were proven in the case of finite horizon by (Faggian, 2005b) and (Faggian, 2008a). The case of infinite horizon is more challenging as a mathematical problem, and indeed more interesting from the point of view of optimal investment models with vintage capital, where what mainly matters is the behavior of optimal trajectories and controls in the long run. Finally it is explained how the results can be applied to improve the analysis of the optimal paths previously performed by Barucci and Gozzi and by Feichtinger et al.
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- 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," Other publications TiSEM 3fc960b5-8f69-4008-a3e4-4, Tilburg University, School of Economics and Management.
- 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).
- 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 & LICANDRO, Omar & PUCH, Luis A. & DEL RIO, Fernando, "undated". "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).
- 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, "undated". "Vintage capital and the dynamics of the AK model," Working Papers 2000-01, FEDEA.
- 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.
- 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.
- 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.
- 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., 2006. "Anticipation effects of technological progress on capital accumulation : A vintage capital approach," Other publications TiSEM 9a8debb0-5030-46fa-b89e-b, Tilburg University, School of Economics and Management.
- Benhabib, Jess & Rustichini, Aldo, 1990.
"Vintage Capital, Investment And Growth,"
90-22, C.V. Starr Center for Applied Economics, New York University.
- Silvia Faggian, 2008. "Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital," Working Papers 181, Department of Applied Mathematics, Università Ca' Foscari Venezia.
- Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
- 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.
- Chari, V V & Hopenhayn, Hugo, 1991. "Vintage Human Capital, Growth, and the Diffusion of New Technology," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1142-1165, December.
- Silvia Faggian, 2008. "Equilibrium Points for Optimal Investment with Vintage Capital," Working Papers 182, Department of Applied Mathematics, Università Ca' Foscari Venezia.
- Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
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