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Turnpike and Optimal Trajectories in Integral Dynamic Models with Endogenous Delay

Author

Listed:
  • N. Hritonenko

    (Prairie View A&M University)

  • Yu. Yatsenko

    (Houston Baptist University)

Abstract

Nonlinear optimal control of dynamic systems with endogenous time delays is analyzed. Such systems have important applications and are described by Volterra integral equations with unknowns in the integration limits. The paper focuses on the structure and asymptotic behavior of solutions to several optimization problems with endogenous delay. It is shown that, in certain cases, a special delay trajectory exists and attracts the optimal solution. In economics, such behavior corresponds to the turnpike properties of the optimal lifetime of capital in vintage capital models.

Suggested Citation

  • N. Hritonenko & Yu. Yatsenko, 2005. "Turnpike and Optimal Trajectories in Integral Dynamic Models with Endogenous Delay," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 109-127, October.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:1:d:10.1007_s10957-005-6395-2
    DOI: 10.1007/s10957-005-6395-2
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    Citations

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    Cited by:

    1. Natali Hritonenko & Yuri Yatsenko, 2008. "From Linear to Nonlinear Utility in Vintage Capital Models," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 230-248.
    2. Raouf Boucekkine & Giorgio Fabbri & Patrick-Antoine Pintus, 2011. "On the optimal control of a linear neutral differential equation arising in economics," Working Papers halshs-00576770, HAL.
    3. Boucekkine Raouf & Hritonenko Natali & Yatsenko Yuri, 2013. "On the Optimal Control of the Vintage Capital Growth Model with Endogenous Labour Supply," Mathematical Economics Letters, De Gruyter, vol. 1(1), pages 3-7, October.
    4. 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).
    5. Yuri Yatsenko, 2009. "Price vs. Quantity Regulation and Technological Modernization," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 8(3), pages 255-258, December.
    6. Roberto M. Samaniego & Juliana Yu Sun, 2022. "The Embodiment Controversy: On the Policy Implications of Vintage Capital Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 54(5), pages 1175-1222, August.
    7. Yu. Yatsenko & N. Hritonenko, 2007. "Network economics and optimal replacement of age-structured IT capital," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 483-497, June.
    8. Raouf Boucekkine & Natali Hritonenko & Yuri Yatsenko, "undated". "Optimal Firm Behavior under Environmental Constraints," Working Papers 2008_11, Business School - Economics, University of Glasgow.
    9. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, vol. 147(2), pages 551-569.
    10. HRITONENKO, Natali & YATSENKO, Yuri, 2011. "Sustainable growth and modernization under environmental hazard and adaptation," LIDAM Discussion Papers CORE 2011025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Alexander J. Zaslavski, 2023. "An Optimal Control Problem Related to the RSS Model," Mathematics, MDPI, vol. 11(17), pages 1-14, September.
    12. 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).
    13. BOUCEKKINE, Raouf & FABBRI, Giorgio & PINTUS, Patrick, 2012. "On the optimal control of a linear neutral differential equation arising in economics," LIDAM Reprints CORE 2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Kredler, Matthias, 2014. "Vintage human capital and learning curves," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 154-178.
    15. Boucekkine, Raouf & Hritonenko, Natali & Yatsenko, Yuri, 2011. "Scarcity, regulation and endogenous technical progress," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 186-199, March.

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