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Multiple Solutions in Systems of Functional Differential Equations

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  • Hippolyte D'Albis

    ()
    (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Emmanuelle Augeraud-Véron

    ()
    (MIA - Mathématiques, Image et Applications - Université de La Rochelle : EA3165)

  • Hermen Jan Hupkes

    ()
    (University of Missouri - Columbia - Mathematics Department)

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. The obtained conditions represent the counterpart of the Blanchard and Kahn conditions for the considered functional equations.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00786419.

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Date of creation: Jan 2013
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Handle: RePEc:hal:cesptp:halshs-00786419

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Related research

Keywords: Delay differential equation; advance differential equations; existence; indeterminacy;

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References

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  1. Hippolyte D'Albis & Emmanuelle Augeraud-Véron & Alain Venditti, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717198, HAL.
  2. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2009. "Maintenance and investment: complements or substitutes? A reappraisal," Working Papers, Business School - Economics, University of Glasgow 2009_21, Business School - Economics, University of Glasgow.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Raouf Boucekkine & David De La Croix & Omar Licandro, 2004. "MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 151-179.
  8. 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.
  9. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, Elsevier, vol. 104(2), pages 340-375, June.
  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. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(2-3), pages 347-362.
  12. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(2), pages 551-569.
  13. 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.
  14. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(3), pages 380-396, December.
  15. Raouf Boucekkine & David de la Croix & Omar Licandro, . "vintage human capital, demographic trends and endogenous growth," Working Papers 2000-02, FEDEA.
  16. Willem H. Buiter, 1984. "Saddlepoint Problems in Contifuous Time Rational Expectations Models: A General Method and Some Macroeconomic Ehamples," NBER Technical Working Papers 0020, National Bureau of Economic Research, Inc.
  17. repec:hal:journl:halshs-00717198 is not listed on IDEAS
  18. Raouf Boucekkine & David de la Croix & Omar Licandro, . "Modelling vintage structures with DDEs: Principles and applications," Working Papers 2004-07, FEDEA.
  19. 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.
  20. 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.
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Cited by:
  1. 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.
  2. 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.

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