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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.

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  • 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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    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. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2018. "Geographic environmental Kuznets curves: The optimal growth linear-quadratic case," Working Papers 2018-10, Grenoble Applied Economics Laboratory (GAEL).
    3. Jamsheed Shorish, 2007. "Welfare analysis of HIV/AIDS: Formulating and computing a continuous time overlapping generations policy model," Economics Discussion Paper Series 0709, Economics, The University of Manchester.
    4. 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.
    5. 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.
    6. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
    7. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    8. Galo Nuno & Benjamin Moll, 2018. "Social Optima in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 150-180, April.
    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. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    11. 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.
    12. 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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