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Multiple Solutions in Systems of Functional Differential Equations

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  • d'Albis, Hippolyte
  • Augeraud-Véron, Emmanuelle
  • Hupkes, Herman Jan

Abstract

This paper proposes conditions for the existence and uniqueness of solutions to systems of linear differential or algebraic equations with delays or advances, in which some variables may be non-predetermined. These conditions represent the counterpart to the Blanchard and Kahn conditions for the functional equations under consideration. To illustrate the mathematical results, applications to an overlapping generations model and a time-to-build model are developed.

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File URL: http://mpra.ub.uni-muenchen.de/54777/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 54777.

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Date of creation: 25 Mar 2014
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Handle: RePEc:pra:mprapa:54777

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Keywords: Delay Differential Equations; Advance Differential Equations; Existence; Indeterminacy;

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  1. Buiter, Willem H, 1984. "Saddlepoint Problems in Continuous Time Rational Expectations Models: A General Method and Some Macroeconomic Examples," Econometrica, Econometric Society, Econometric Society, vol. 52(3), pages 665-80, May.
  2. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(3), pages 380-396, December.
  3. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, Elsevier, vol. 143(1), pages 331-373, November.
  4. Raouf, BOUCEKKINE & David de la Croix & Omar Lidandro, 2004. "Modelling vintage structures with DDEs : principles and applications," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 2004004, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  5. Hippolyte D'Albis & Emmanuelle Augeraud-Véron & Alain Venditti, 2009. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Working Papers halshs-00432267, HAL.
  6. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 23(8), pages 1155-1175, August.
  7. Raouf Boucekkine & David de la Croix & Omar Licandro, . "Modelling vintage structures with DDEs: Principles and applications," Working Papers 2004-07, FEDEA.
  8. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2000. "Vintage Human Capital, Demographic Trends and Endogenous Growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 2000007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  9. El-Hodiri, Mohamed A & Loehman, Edna & Whinston, Andrew B, 1972. "An Optimal Growth Model with Time Lags," Econometrica, Econometric Society, Econometric Society, vol. 40(6), pages 1137-46, November.
  10. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006, Society for Computational Economics 77, Society for Computational Economics.
  11. Raouf BOUCEKKINE & Giorgio FABBRI & Fausto GOZZI, 2009. "Maintenance and investment : Complements or Substitutes ? A Reappraisal," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 2009010, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  12. Hippolyte D'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Funtional Differential-Algebraic Equations of Mixed Type," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717412, HAL.
  13. Gray, Malcolm R & Turnovsky, Stephen J, 1979. "Expectational Consistency, Informational Lags, and the Formulation of Expectations in Continuous Time Models," Econometrica, Econometric Society, Econometric Society, vol. 47(6), pages 1457-74, November.
  14. Raouf Boucekkine & Omar Licandro & Christopher Paul, . "Differential-Difference Equations in Economics: On the Numerical Solution of Vintage Capital Growth Models," Computing in Economics and Finance 1996, Society for Computational Economics _036, Society for Computational Economics.
  15. Raouf Boucekkine & David de la Croix & Omar Licandro, . "vintage human capital, demographic trends and endogenous growth," Working Papers 2000-02, FEDEA.
  16. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(2), pages 551-569.
  17. Bambi, Mauro & Fabbri, Giorgio & Gozzi, Fausto, 2009. "Optimal policy and consumption smoothing effects in the time-to-build AK model," MPRA Paper 17128, University Library of Munich, Germany.
  18. Benhabib, Jess, 2004. "Interest Rate Policy in Continuous Time with Discrete Delays," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 36(1), pages 1-15, February.
  19. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2013. "Bounded Interest Rate Feedback Rules in Continuous-Time," MPRA Paper 45424, University Library of Munich, Germany.
  20. repec:hal:journl:halshs-00717198 is not listed on IDEAS
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Citations

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Cited by:
  1. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Bounded interest rate feedback rules in continuous-time," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 39(C), pages 227-236.
  2. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Herman Jan, 2014. "Stability and Determinacy Conditions for Mixed-type Functional Differential Equations," MPRA Paper 56600, University Library of Munich, Germany.

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