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Optimal Harvesting of Stochastically Fluctuating Populations Driven by a Generalized Logistic SDE Growth Model

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  • Nuno M. Brites

    (ISEG-School of Economics and Management, Universidade de Lisboa, 1649-004 Lisbon, Portugal
    REM—Research in Economics and Mathematics, CEMAPRE, Rua do Quelhas, 6, Gabinete 503, 1200-781 Lisboa, Portugal)

Abstract

We describe the growth dynamics of a stock using stochastic differential equations with a generalized logistic growth model which encompasses several well-known growth functions as special cases. For each model, we compute the optimal variable effort policy and compare the expected net present value of the total profit earned by the harvester among policies. In addition, we further extend the study to include parameters sensitivity, such as the costs and volatility, and present an explicitly Crank–Nicolson discretization scheme necessary to obtain optimal policies.

Suggested Citation

  • Nuno M. Brites, 2022. "Optimal Harvesting of Stochastically Fluctuating Populations Driven by a Generalized Logistic SDE Growth Model," Mathematics, MDPI, vol. 10(17), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3098-:d:900405
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    References listed on IDEAS

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    1. Alvarez, Luis H. R., 2000. "Singular stochastic control in the presence of a state-dependent yield structure," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 323-343, April.
    2. Nuno M. Brites & Carlos A. Braumann, 2020. "Stochastic differential equations harvesting policies: Allee effects, logistic‐like growth and profit optimization," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(5), pages 825-835, September.
    3. M. A. Shah & Usha Sharma, 2003. "Optimal harvesting policies for a generalized Gordon–Schaefer model in randomly varying environment," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 19(1), pages 43-49, January.
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