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On Dynamic Programming in Economic Models Governed by DDEs

Author

Listed:
  • GIORGIO FABBRI
  • SILVIA FAGGIAN
  • FAUSTO GOZZI

Abstract

A family of optimal control problems for economic models, where state variables are driven by delay differential equations (DDEs) and subject to constraints, is treated by Bellman's dynamic programming in infinite dimensional spaces. An existence theorem is provided for the associated Hamilton-Jacobi-Bellman (HJB) equation: the value function of the control problem solves the HJB equation in a suitable sense (although such value function cannot be computed explicitly). An AK model with vintage capital and an advertising model with delay effect are taken as examples.

Suggested Citation

  • Giorgio Fabbri & Silvia Faggian & Fausto Gozzi, 2008. "On Dynamic Programming in Economic Models Governed by DDEs," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 267-290.
    • Handle: RePEc:taf:mpopst:v:15:y:2008:i:4:p:267-290
    DOI: 10.1080/08898480802440836
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    Citations

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    Cited by:

    1. 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).
    2. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
    3. 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.
    4. Urszula Foryś & Jan Poleszczuk & Ting Liu, 2014. "Logistic Tumor Growth with Delay and Impulsive Treatment," Mathematical Population Studies, Taylor & Francis Journals, vol. 21(3), pages 146-158, September.

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