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Optimal Harvest under a Gilpin-Ayala Model Driven by the Hawkes Process

Author

Listed:
  • Nyassoke Titi Gaston Clément

    (Université de Douala)

  • Sadefo Kamdem Jules

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

  • Fono Louis Aimé

    (Faculté des Sciences [Douala] - Université de Douala)

Abstract

This paper analyzes the optimal effort for a risk-averse fisherman where the biomass process follows a Hawkes jump-diffusion process with Gilpin-Ayala drift. The main feature of the Hawkes process is to capture the phenomenon of clustering. The price process is of the mean-reverting type. We prove a sufficient maximum principle for the optimal control of a stochastic system consisting of an SDE driven by the Hawkes process and, by the concavity of the Hamiltonian, we obtain the optimal effort of the fisherman for a risk-averse investor.

Suggested Citation

  • Nyassoke Titi Gaston Clément & Sadefo Kamdem Jules & Fono Louis Aimé, 2025. "Optimal Harvest under a Gilpin-Ayala Model Driven by the Hawkes Process," Post-Print hal-04987283, HAL.
    • Handle: RePEc:hal:journl:hal-04987283
    DOI: 10.1016/j.rinam.2025.100564
    Note: View the original document on HAL open archive server: https://hal.science/hal-04987283v1
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