IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v161y2014i3d10.1007_s10957-013-0451-0.html
   My bibliography  Save this article

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

Author

Listed:
  • Xiaoling Zou

    (Harbin Institute of Technology)

  • Ke Wang

    (Harbin Institute of Technology
    Northeast Normal University)

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.

Suggested Citation

  • Xiaoling Zou & Ke Wang, 2014. "Optimal Harvesting for a Logistic Population Dynamics Driven by a Lévy Process," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 969-979, June.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0451-0
    DOI: 10.1007/s10957-013-0451-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0451-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-013-0451-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kunita, Hiroshi, 2010. "Itô's stochastic calculus: Its surprising power for applications," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 622-652, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    2. Liu, Meng & Bai, Chuanzhi, 2016. "Dynamics of a stochastic one-prey two-predator model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 308-321.
    3. Oscar García, 2019. "Estimating reducible stochastic differential equations by conversion to a least-squares problem," Computational Statistics, Springer, vol. 34(1), pages 23-46, March.
    4. Biane, Philippe, 2010. "Itô's stochastic calculus and Heisenberg commutation relations," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 698-720, May.
    5. Zhao, Yu & Yuan, Sanling, 2017. "Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 20-33.
    6. Kang, Yuanbao & Wang, Caishi, 2014. "Itô formula for one-dimensional continuous-time quantum random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 154-162.
    7. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.
    8. Ishikawa, Yasushi & Kunita, Hiroshi & Tsuchiya, Masaaki, 2018. "Smooth density and its short time estimate for jump process determined by SDE," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3181-3219.
    9. Zhang, Xinhong & Li, Wenxue & Liu, Meng & Wang, Ke, 2015. "Dynamics of a stochastic Holling II one-predator two-prey system with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 571-582.
    10. Gao, Miaomiao & Jiang, Daqing, 2019. "Analysis of stochastic multimolecular biochemical reaction model with lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 601-613.
    11. Wang, Hui & Pan, Fangmei & Liu, Meng, 2019. "Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 591-606.
    12. Tan, Li & Jin, Wei & Hou, Zhenting, 2013. "Weak convergence of functional stochastic differential equations with variable delays," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2592-2599.
    13. Okhrati, Ramin & Balbás, Alejandro & Garrido, José, 2014. "Hedging of defaultable claims in a structural model using a locally risk-minimizing approach," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2868-2891.
    14. Jorge Sanchez-Ortiz & Omar U. Lopez-Cresencio & Francisco J. Ariza-Hernandez & Martin P. Arciga-Alejandre, 2021. "Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative," Mathematics, MDPI, vol. 9(13), pages 1-10, June.
    15. Liu, Meng & Bai, Chuanzhi, 2016. "Optimal harvesting of a stochastic mutualism model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 301-309.
    16. Liu, Meng & Deng, Meiling & Du, Bo, 2015. "Analysis of a stochastic logistic model with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 169-182.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0451-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.