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Equilibrium Points for Optimal Investment with Vintage Capital

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Author Info

  • Silvia Faggian

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

Abstract

The 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.

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File URL: http://virgo.unive.it/wpideas/storage/2008wp182.pdf
File Function: First version, 2008
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Bibliographic Info

Paper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 182.

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Length: 19 pages
Date of creation: Nov 2008
Date of revision:
Handle: RePEc:vnm:wpaper:182

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Related research

Keywords: Linear convex control; Boundary control; Hamilton–Jacobi–Bellman equations; Optimal investment problems; Vintage capital;

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References

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  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. 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, Elsevier, vol. 126(1), pages 143-164, January.
  3. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, INFORMS, vol. 40(2), pages 195-226, February.
  4. 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.
  5. Raouf BOUCEKKINE & Omar LICANDRO & Luis A. PUCH & Fernando DEL RIO, 2002. "Vintage Capital And the Dynamics of the AK Model," Economics Working Papers, European University Institute ECO2002/07, European University Institute.
  6. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, Springer, vol. 74(1), pages 1-38, February.
  7. Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Veliov, V., 2001. "Dynamic Investment Behavior Taking into Account Ageing of the Capital Good," Discussion Paper, Tilburg University, Center for Economic Research 2001-13, Tilburg University, Center for Economic Research.
  8. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, Elsevier, vol. 52(2), pages 159-188, June.
  9. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, . "Vintage capital and the dynamics of the AK model," Working Papers 2000-01, FEDEA.
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Cited by:
  1. Silvia Faggian & Fausto Gozzi, 2008. "Optimal investment models with vintage capital: Dynamic Programming approach," Working Papers, Department of Applied Mathematics, Università Ca' Foscari Venezia 174, Department of Applied Mathematics, Università Ca' Foscari Venezia.

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