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

Nuno M. Brites ()
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Nuno M. Brites: ISEG-School of Economics and Management, Universidade de Lisboa, 1649-004 Lisbon, Portugal

Mathematics, 2022, vol. 10, issue 17, 1-15

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.

Keywords: Crank–Nicolson scheme; harvesting policies; Hamilton–Jacobi–Bellman equation; generalized logistic; stochastic optimal control; profit optimization; stochastic differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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