IDEAS home Printed from https://ideas.repec.org/a/taf/mpopst/v11y2004i3-4p233-270.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/08898480490513625
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/08898480490513625?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    2. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    3. 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, France.
    4. 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.
    5. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    6. 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.
    7. 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.
    8. 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.
    9. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
    10. Shorish, Jamsheed, 2007. "Welfare Analysis of HIV/AIDS: Formulating and Computing a Continuous Time Overlapping Generations Policy Model," Economics Series 211, Institute for Advanced Studies.
    11. 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.
    12. Silvia Faggian, 2008. "Equilibrium Points for Optimal Investment with Vintage Capital," Working Papers 182, Department of Applied Mathematics, Università Ca' Foscari Venezia.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    2. 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.
    3. Silvia Faggian, 2008. "Equilibrium Points for Optimal Investment with Vintage Capital," Working Papers 182, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    4. Philipp Afèche & Mojtaba Araghi & Opher Baron, 2017. "Customer Acquisition, Retention, and Service Access Quality: Optimal Advertising, Capacity Level, and Capacity Allocation," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 674-691, October.
    5. Navdeep Sahni, 2015. "Effect of temporal spacing between advertising exposures: Evidence from online field experiments," Quantitative Marketing and Economics (QME), Springer, vol. 13(3), pages 203-247, September.
    6. Mauro Bambi & Cristina Girolami & Salvatore Federico & Fausto Gozzi, 2017. "Generically distributed investments on flexible projects and endogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 521-558, February.
    7. Prasad A. Naik & Murali K. Mantrala & Alan G. Sawyer, 1998. "Planning Media Schedules in the Presence of Dynamic Advertising Quality," Marketing Science, INFORMS, vol. 17(3), pages 214-235.
    8. Richards, Timothy J. & Patterson, Paul M., 2000. "New Varieties And The Returns To Commodity Promotion: The Case Of Fuji Apples," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 29(01), pages 1-14, April.
    9. G. Bertuzzi & L. Lambertini, 2001. "Advertising in a Differential Game of Spatial Competition," Working Papers 400, Dipartimento Scienze Economiche, Universita' di Bologna.
    10. Julián David Parada, 2008. "Tasa de depreciación endógena y crecimiento económico," Documentos de Trabajo 4594, Universidad del Rosario.
    11. Jorgensen, Steffen & Kort, Peter M., 2002. "Optimal pricing and inventory policies: Centralized and decentralized decision making," European Journal of Operational Research, Elsevier, vol. 138(3), pages 578-600, May.
    12. Luca Lambertini, 2007. "Dynamic Spatial Monopoly with Product Development," Spatial Economic Analysis, Taylor & Francis Journals, vol. 2(2), pages 157-166.
    13. Richards, Timothy J. & Patterson, Paul M., 1998. "New Varieties and the Returns to Commodity Promotion: Washington Fuji Apples," Working Papers 28541, Arizona State University, Morrison School of Agribusiness and Resource Management.
    14. Kort, P.M. & Feichtinger, G. & Hartl, R.F. & Haunschmied, J.L., 1996. "Optimal Enforcement Policies (Crackdowns) on a Drug Market," Other publications TiSEM 8f874586-670a-470a-95a6-b, Tilburg University, School of Economics and Management.
    15. H. Dharma Kwon & Hongzhong Zhang, 2015. "Game of Singular Stochastic Control and Strategic Exit," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 869-887, October.
    16. Kredler, Matthias, 2014. "Vintage human capital and learning curves," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 154-178.
    17. Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Veliov, V., 2001. "Dynamic Investment Behavior Taking into Account Ageing of the Capital Good," Other publications TiSEM 1e12e7c6-11c2-4632-a8e2-1, Tilburg University, School of Economics and Management.
    18. Luca Lambertini, 2014. "Dynamic Analysis of an Electoral Campaign," Dynamic Modeling and Econometrics in Economics and Finance, in: Josef Haunschmied & Vladimir M. Veliov & Stefan Wrzaczek (ed.), Dynamic Games in Economics, edition 127, pages 187-204, Springer.
    19. L. Colombo & L. Lambertini, 2003. "Dynamic Advertising Under Vertical Product Differentiation," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 261-280, November.
    20. M'ed'eric Motte & Huy^en Pham, 2021. "Optimal bidding strategies for digital advertising," Papers 2111.08311, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:mpopst:v:11:y:2004:i:3-4:p:233-270. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GMPS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.