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Optimal Renewable Resource Harvesting model using price and biomass stochastic variations: A Utility Based Approach

Author

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  • Gaston Clément Nyassoke Titi

    (Université de Douala)

  • Jules Sadefo-Kamdem

    (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

  • Louis Aimé Fono

    (Université de Douala)

Abstract

In this article, we provide a general framework for analyzing the optimal harvest of a renewable resource(i.e. fish, shrimp) assuming that the price and biomass evolve stochastically and harvesters have a constantrelative risk aversion (CRRA) . In order to take into account the impact of a sudden change in the environ-ment linked to the ecosystem, we assume that the biomass are governed by a stochastic differential equationof the ‘Gilpin-Ayala' type, with regime change in the parameters of the drift and variance. Under the aboveassumptions, we find the optimal effort to be deployed by the collector (fishery for example) in order tomaximize the expected utility of its profit function. To do this, we give the proof of the existence anduniqueness of the value function, which is derived from the Hamilton-Jacobi-Bellman equations associatedwith this problem, by resorting to a definition of the viscosity solution.

Suggested Citation

  • Gaston Clément Nyassoke Titi & Jules Sadefo-Kamdem & Louis Aimé Fono, 2022. "Optimal Renewable Resource Harvesting model using price and biomass stochastic variations: A Utility Based Approach," Post-Print hal-03169348, HAL.
    • Handle: RePEc:hal:journl:hal-03169348
    DOI: 10.1007/s00186-022-00782-0
    Note: View the original document on HAL open archive server: https://hal.science/hal-03169348v3
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    References listed on IDEAS

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    1. Gaston Clément Nyassoke Titi & Jules Sadefo Kamdem & Louis Fono, 2020. "Fishery Management in a Regime Switching Environment: Utility Based Approach," Post-Print hal-02923728, HAL.
    2. Li, Dingshi, 2013. "The stationary distribution and ergodicity of a stochastic generalized logistic system," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 580-583.
    3. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
    4. Harold Hotelling, 1931. "The Economics of Exhaustible Resources," Journal of Political Economy, University of Chicago Press, vol. 39(2), pages 137-137.
    5. Gaston Clément Nyassoke Titi & Jules Sadefo-Kamdem & Louis Aimé Fono, 2020. "Fishery Management in a Regime Switching Environment: Utility Based Approach," Working Papers hal-02433395, HAL.
    6. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
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    Cited by:

    1. Sabarathinam Srinivasan & Suresh Kumarasamy & Zacharias E. Andreadakis & Pedro G. Lind, 2023. "Artificial Intelligence and Mathematical Models of Power Grids Driven by Renewable Energy Sources: A Survey," Energies, MDPI, vol. 16(14), pages 1-56, July.

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    More about this item

    Keywords

    Stochastic Gilpin-Ayala; CRRA utility; Viscosity solutions; Renewable Resources; Optimal Effort;
    All these keywords.

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