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

Nyassoke Titi Gaston Clément, Sadefo Kamdem Jules and Fono Louis Aimé
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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

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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.

Keywords: Stochastic Gilpin-Ayala; self-exciting Hawkes process; Sufficient maximum principle; Optimal Effort (search for similar items in EconPapers)
Date: 2025
Note: View the original document on HAL open archive server: https://hal.science/hal-04987283v1
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Published in Results in Applied Mathematics, 2025, 26, pp.100564. ⟨10.1016/j.rinam.2025.100564⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04987283

DOI: 10.1016/j.rinam.2025.100564

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