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Multiple solutions in systems of functional differential equations

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  • d’Albis, Hippolyte
  • Augeraud-Véron, Emmanuelle
  • Hupkes, Hermen 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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 52 (2014)
Issue (Month): C ()
Pages: 50-56

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Handle: RePEc:eee:mateco:v:52:y:2014:i:c:p:50-56

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Delay differential equations; Advance differential equations; Existence; Indeterminacy;

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  1. Mauro BAMBI & Giorgio FABBRI & Fausto GOZZI, 2010. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales), Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) 2010029, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  2. Raouf BOUCEKKINE & David DE LA CROIX & Omar LICANDRO, 2004. "Modelling vintage structures with DDEs: principles and applications," Economics Working Papers, European University Institute ECO2004/06, European University Institute.
  3. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(3), pages 380-396, December.
  4. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers, European University Institute ECO2006/17, European University Institute.
  5. 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), HAL halshs-00717412, HAL.
  6. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Venditti, Alain, 2010. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," LERNA Working Papers, LERNA, University of Toulouse 10.13.319, LERNA, University of Toulouse.
  7. 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.
  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. 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.
  10. 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).
  11. Patrick Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," UCLA Economics Working Papers, UCLA Department of Economics 767, UCLA Department of Economics.
  12. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(2), pages 551-569.
  13. BOUCEKKINE, Raouf & FABBRI, Giorgio & GOZZI, Fausto, . "Maintenance and investment: complements or substitutes? A reappraisal," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -2333, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. 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.
  15. 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.
  16. repec:hal:journl:halshs-00717198 is not listed on IDEAS
  17. 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.
  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.
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Cited by:
  1. 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.
  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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