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Dynamic stochastic optimization for sustainability and management of overconsumption

Author

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  • Rosella Castellano

    (UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome])

  • Roy Cerqueti

    (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

Abstract

This paper deals with an intergenerational utility maximization problem for consuming a naturally exhaustible resource. In this context, we are at odds with the unfair standard procedure of applying a time-dependent factor for discounting the utility and introducing a suitable function for penalizing overconsumption. A finite-time horizon dynamic stochastic optimization problem is presented to achieve the desired target. We provide a closed-form solution to the problem which does not lead forcefully to the classical golden rule outcome of not consuming now to save the future. The theoretical findings are validated through extensive numerical experiments, with a parameter set selected based on empirical data. Such experiments highlight that optimal consumption depends strongly on the natural resource regeneration rate and the initial value of the stock.

Suggested Citation

  • Rosella Castellano & Roy Cerqueti, 2025. "Dynamic stochastic optimization for sustainability and management of overconsumption," Post-Print hal-05108867, HAL.
    • Handle: RePEc:hal:journl:hal-05108867
    DOI: 10.1016/j.cnsns.2025.108960
    Note: View the original document on HAL open archive server: https://univ-angers.hal.science/hal-05108867v1
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