Advanced Search
MyIDEAS: Login

Optimal investment models with vintage capital: Dynamic Programming approach

Contents:

Author Info

  • Silvia Faggian

    ()
    (Department of Applied Mathematics, University of Venice)

  • Fausto Gozzi

    ()
    (LUISS Guido Carli)

Abstract

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 (see e.g. [11, 12], [30, 32]) 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 in [26][27]. 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. The study of infinite horizon is performed through a nontrivial limiting procedure from the corresponding finite horizon problems

Download Info

If 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.
File URL: http://virgo.unive.it/wpideas/storage/2008wp174.pdf
File Function: First version, 2008
Download Restriction: no

Bibliographic Info

Paper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 174.

as in new window
Length: 34 pages
Date of creation: Nov 2008
Date of revision:
Handle: RePEc:vnm:wpaper:174

Contact details of provider:
Postal: Dorsoduro, 3825/E, 30123 Venezia
Phone: ++39 041 2346910-6911
Fax: ++ 39 041 5221756
Web page: http://www.dma.unive.it/
More information through EDIRC

Related research

Keywords: Optimal investment; vintage capital; age-structured systems; optimal control; dynamic programming; Hamilton-Jacobi-Bellman equations; linear convex control; boundary control;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
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.:
as in new window
  1. 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.
  2. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
  3. Boucekkine, Raouf & Del Rio, Fernando & Licandro, Omar, 2000. "Vintage capital and the dynamics of the AK model," CEPREMAP Working Papers (Couverture Orange) 0003, CEPREMAP.
  4. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
  5. 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.
  6. 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.
  7. Silvia Faggian, 2008. "Equilibrium Points for Optimal Investment with Vintage Capital," Working Papers 182, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  8. 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 1142-65, December.
  9. 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.
  10. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Silvia Faggian & Giorgio Fabbri & Giuseppe Freni, 2013. "On the Mitra--Wan Forest Management Problem in Continuous Time," Working Papers 2013:28, Department of Economics, University of Venice "Ca' Foscari".
  2. Raouf Boucekkine & David de la Croix & Omar Licandro, 2011. "Vintage capital growth theory: Three breakthroughs," UFAE and IAE Working Papers 875.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  3. Silvia Faggian & Luca Grosset, 2013. "Optimal advertising strategies with age-structured goodwill," Computational Statistics, Springer, vol. 78(2), pages 259-284, October.
  4. Raouf Boucekkine & David De La Croix & Omar Licandro, 2011. "Vintage capital theory: Three breakthroughs," Working Papers halshs-00599074, HAL.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:vnm:wpaper:174. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marco LiCalzi).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.