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

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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.

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Acknowledgements

The authors sincerely thank the editors and the anonymous reviewers for their valuable comments that have led to the present improved version of the original manuscript. This research was partially supported by grants Nos. 11171081, 11171056, 11301112 and 11301207 from the National Natural Science Foundation of P.R. China.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, P.R. China

    Xiaoling Zou & Ke Wang

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P.R. China

    Ke Wang

Authors
  1. Xiaoling Zou
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  2. Ke Wang
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Correspondence to Xiaoling Zou.

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Communicated by Mimmo Iannelli.

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Zou, X., Wang, K. Optimal Harvesting for a Logistic Population Dynamics Driven by a Lévy Process. J Optim Theory Appl 161, 969–979 (2014). https://doi.org/10.1007/s10957-013-0451-0

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  • DOI: https://doi.org/10.1007/s10957-013-0451-0

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