Fishery management in a regime switching environment: Utility theory approach
In this paper, we study the problem of optimal fishing for regime switching in the growth dynamics of a given fish species which is described by the differential stochastic logistic model with two states: prior or during floods and after. The resulting dynamic programming principle leads to a system...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-08-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037420300352 |
| _version_ | 1818339771697594368 |
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| author | Gaston Clément Nyassoke Titi Jules Sadefo Kamdem Louis Aimé Fono |
| author_facet | Gaston Clément Nyassoke Titi Jules Sadefo Kamdem Louis Aimé Fono |
| author_sort | Gaston Clément Nyassoke Titi |
| collection | DOAJ |
| description | In this paper, we study the problem of optimal fishing for regime switching in the growth dynamics of a given fish species which is described by the differential stochastic logistic model with two states: prior or during floods and after. The resulting dynamic programming principle leads to a system of two variational inequalities. By using viscosity solutions approach, we prove the existence and uniqueness of the value functions. Then numerical approximation of the obtained system is used to determine the optimal fishing effort for a sustainable fishery. |
| first_indexed | 2024-12-13T15:32:18Z |
| format | Article |
| id | doaj.art-c4a47880662641b781dc6ae43946be21 |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-12-13T15:32:18Z |
| publishDate | 2020-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-c4a47880662641b781dc6ae43946be212022-12-21T23:40:09ZengElsevierResults in Applied Mathematics2590-03742020-08-017100125Fishery management in a regime switching environment: Utility theory approachGaston Clément Nyassoke Titi0Jules Sadefo Kamdem1Louis Aimé Fono2Laboratoire de Mathématiques, Faculté des Sciences, Université de Douala, Cameroon; Corresponding author.MRE EA 7491, Université de Montpellier, France; DFR SJE, Université de la Guyane, French GuianaLaboratoire de Mathématiques, Faculté des Sciences, Université de Douala, CameroonIn this paper, we study the problem of optimal fishing for regime switching in the growth dynamics of a given fish species which is described by the differential stochastic logistic model with two states: prior or during floods and after. The resulting dynamic programming principle leads to a system of two variational inequalities. By using viscosity solutions approach, we prove the existence and uniqueness of the value functions. Then numerical approximation of the obtained system is used to determine the optimal fishing effort for a sustainable fishery.http://www.sciencedirect.com/science/article/pii/S2590037420300352Regime switchingCrra utilityStochastic logistic growthMean-reverting pricesViscosity solutionHoward’s algorithm |
| spellingShingle | Gaston Clément Nyassoke Titi Jules Sadefo Kamdem Louis Aimé Fono Fishery management in a regime switching environment: Utility theory approach Results in Applied Mathematics Regime switching Crra utility Stochastic logistic growth Mean-reverting prices Viscosity solution Howard’s algorithm |
| title | Fishery management in a regime switching environment: Utility theory approach |
| title_full | Fishery management in a regime switching environment: Utility theory approach |
| title_fullStr | Fishery management in a regime switching environment: Utility theory approach |
| title_full_unstemmed | Fishery management in a regime switching environment: Utility theory approach |
| title_short | Fishery management in a regime switching environment: Utility theory approach |
| title_sort | fishery management in a regime switching environment utility theory approach |
| topic | Regime switching Crra utility Stochastic logistic growth Mean-reverting prices Viscosity solution Howard’s algorithm |
| url | http://www.sciencedirect.com/science/article/pii/S2590037420300352 |
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