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On The Dynamic Programming Approach For Optimal Control Problems Of Pde'S With Age Structure

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  • Silvia Faggian
  • Fausto Gozzi

Abstract

A survey and some new results are presented concerning the dynamic programming for a class of optimal control problems of partial differential equations with age-structure and of delay systems that include some applied examples from economic theory and from population dynamics. A general optimal control problem in Hilbert spaces applying to all examples is investigated, with particular stress on one family of applications: optimal investment models with vintage capital. Some new results are given for the case of constrained investments, including a study of the properties of the optimal trajectories.

Suggested Citation

  • Silvia Faggian & Fausto Gozzi, 2004. "On The Dynamic Programming Approach For Optimal Control Problems Of Pde'S With Age Structure," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 233-270.
  • Handle: RePEc:taf:mpopst:v:11:y:2004:i:3-4:p:233-270
    DOI: 10.1080/08898480490513625
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    Citations

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    Cited by:

    1. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2015. "On the Mitra–Wan forest management problem in continuous time," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1001-1040.
    2. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2018. "Geographic Environmental Kuznets Curves: The Optimal Growth Linear-Quadratic Case," AMSE Working Papers 1813, Aix-Marseille School of Economics, Marseille, France.
    3. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    4. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    5. repec:red:issued:15-330 is not listed on IDEAS
    6. Jamsheed Shorish, 2007. "Welfare analysis of HIV/AIDS: Formulating and computing a continuous time overlapping generations policy model," The School of Economics Discussion Paper Series 0709, Economics, The University of Manchester.
    7. Goetz, Renan-Ulrich & Hritonenko, Natali & Yatsenko, Yuri, 2008. "The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 3032-3053, September.
    8. Fabbri, Giorgio & Faggian, Silvia & Gozzi, Fausto, 2006. "On the Dynamic Programming approach to economic models governed by DDE's," MPRA Paper 2825, University Library of Munich, Germany.
    9. Fabbri, Giorgio & Gozzi, Fausto & Swiech, Andrzej, 2007. "Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations," MPRA Paper 3547, University Library of Munich, Germany.
    10. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
    11. Silvia Faggian, 2008. "Equilibrium Points for Optimal Investment with Vintage Capital," Working Papers 182, Department of Applied Mathematics, Università Ca' Foscari Venezia.

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