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Optimal Control in Infinite Dimensional Spaces and Economic Modeling: State of the Art and Perspectives

Author

Listed:
  • Giorgio Fabbri

    (Université Grenoble-Alpes, CNRS, INRA)

  • Silvia Faggian

    (Ca’ Foscari University of Venice)

  • Salvatore Federico

    (University of Bologna)

  • Fausto Gozzi

    (Luiss University)

Abstract

This survey collects, within a unified framework, various results (primarily by the authors themselves) on the use of Deterministic Infinite-Dimensional Optimal Control Theory to address applied economic models. The main aim is to illustrate, through several examples, the typical features of such models (including state constraints, non-Lipschitz data, and non-regularizing differential operators) and the corresponding methods needed to handle them. This necessitates developing aspects of the existing Deterministic Infinite-Dimensional Optimal Control Theory (see, e.g., the book by Li and Yong, 2012) in specific and often nontrivial directions. Given the breadth of this area, we emphasize the Dynamic Programming Approach and its application to problems where explicit or quasi-explicit solutions of the associated Hamilton–Jacobi–Bellman (HJB) equations can be obtained. We also provide insights and references for cases where such explicit solutions are not available.

Suggested Citation

  • Giorgio Fabbri & Silvia Faggian & Salvatore Federico & Fausto Gozzi, 2025. "Optimal Control in Infinite Dimensional Spaces and Economic Modeling: State of the Art and Perspectives," Working Papers 2025: 16, Department of Economics, University of Venice "Ca' Foscari".
    • Handle: RePEc:ven:wpaper:2025:16
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    References listed on IDEAS

    as
    1. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    2. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 635-669, August.
    3. Bambi, Mauro & Gozzi, Fausto, 2020. "Internal habits formation and optimality," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 165-172.
    4. Augeraud-Veron, Emmanuelle & Bambi, Mauro, 2015. "Endogenous growth with addictive habits," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 15-25.
    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. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    7. 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.
    8. Emmanuelle Augeraud-Veron & Mauro Bambi & Fausto Gozzi, 2017. "Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 584-611, May.
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    Cited by:

    1. Filippo de Feo & Fausto Gozzi & Andrzej 'Swik{e}ch & Lukas Wessels, 2025. "Stochastic Optimal Control of Interacting Particle Systems in Hilbert Spaces and Applications," Papers 2511.21646, arXiv.org.

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    Keywords

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E12 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Keynes; Keynesian; Post-Keynesian; Modern Monetary Theory
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity

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