Optimal Harvesting for a Logistic Population Dynamics Driven by a Lévy Process

Xiaoling Zou () and Ke Wang ()
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Xiaoling Zou: Harbin Institute of Technology
Ke Wang: Harbin Institute of Technology

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 3, No 17, 969-979

Abstract: Abstract The optimal harvesting problem for a stochastic logistic jump-diffusion process is studied in this paper. Two kinds of environmental noises are considered in the model. One is called white noise which is described by a standard Brownian motion, and the other is called jumping noise which is described by a Lévy process. For three types of yield functions (time averaging yield, expected yield and sustainable yield), the optimal harvesting efforts, the corresponding maximum yields and the steady states of population mean under optimal harvesting strategy are respectively given. A new equivalent relationship among these three different objective functions is showed by the ergodic method. This method provides a new approach to the optimal harvesting problem. Results in this paper show that environmental noises have important effect on the optimal harvesting problem.

Keywords: Stochastic optimization; Poisson random measure; Dynamic properties; Asymptotically stable in distribution; Ergodic method (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0451-0

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