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Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

Author

Listed:
  • Emmanuelle Augeraud-Veron

    (GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique)

  • Mauro Bambi
  • Fausto Gozzi

Abstract

In this paper, we study an economic model, where internal habits play a role. Their formation is described by a more general functional form than is usually assumed in the literature, because a finite memory effect is allowed. Indeed, the problem becomes the optimal control of a standard ordinary differential equation, with the past of the control entering both the objective function and an inequality constraint. Therefore, the problem is intrinsically infinite dimensional. To solve this model, we apply the dynamic programming approach and we find an explicit solution for the associated Hamilton–Jacobi–Bellman equation, which lets us write the optimal strategies in feedback form. Therefore, we contribute to the existing literature in two ways. Firstly, we fully develop the dynamic programming approach to a type of problem not studied in previous contributions. Secondly, we use this result to unveil the global dynamics of an economy characterized by generic internal habits.

Suggested Citation

  • Emmanuelle Augeraud-Veron & Mauro Bambi & Fausto Gozzi, 2017. "Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension," Post-Print hal-02871232, HAL.
    • Handle: RePEc:hal:journl:hal-02871232
    DOI: 10.1007/s10957-017-1073-8
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    References listed on IDEAS

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    1. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
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    8. Giuseppe Freni & Fausto Gozzi & Neri Salvadori, 2006. "Existence of optimal strategies in linear multisector models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 25-48, September.
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    11. Mauro Bambi & Cristina Di Girolami & Salvatore Federico & Fausto Gozzi, 2014. "On the Consequences of Generically Distributed Investments on Flexible Projects in an Endogenous Growth Model," Discussion Papers 14/15, Department of Economics, University of York.
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    Cited by:

    1. Bambi, Mauro & Gozzi, Fausto, 2020. "Internal habits formation and optimality," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 165-172.
    2. Augeraud-Veron, Emmanuelle & Boucekkine, Raouf & Gozzi, Fausto & Venditti, Alain & Zou, Benteng, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    3. Morhaim, Lisa & Ulus, Ayşegül Yıldız, 2023. "On history-dependent optimization models: A unified framework to analyze models with habits, satiation and optimal growth," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    4. Xuepin Wu & Jiru Han, 2021. "Psychological Needs, Physiological Needs and Regional Comparison Effects," Sustainability, MDPI, vol. 13(16), pages 1-21, August.

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