Advertisement

Non-renewable Fishery Resource Management Under Incomplete Information

  • Hidekazu YoshiokaEmail author
  • Yuta Yaegashi
  • Yumi Yoshioka
  • Kentaro Tsugihashi
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)

Abstract

In this brief paper, stochastic control theory under incomplete information is applied to mathematical modeling of inland fishery management. The inland fishery resource to be managed is non-renewable in the sense that its reproduction is unsuccessful. The incomplete information comes from the uncertain body growth rate of the individuals due to temporal regime-switching of their foods. We show that finding the most cost-effective harvesting policy of the non-renewable fishery resource reduces to solving a Hamilton-Jacobi-Bellman equation. The equation is numerically solved via a simple finite difference scheme focusing on the major inland fishery resource Plecoglossusaltivelis (P. altivelis: Ayu) in Japan.

Notes

Acknowledgements

This work was supported by The River Foundation under grant The River Fund No. 285311020, The Japan Society for the Promotion Science under grant KAKENHI No. 17K15345 and No. 17J09125, and Water Resources Environment Center under grant The WEC Applied Ecology Research Grant No. 2016-02. The authors thank the officers of Hii River Fisheries Cooperatives for providing valuable data and comments for this research.

References

  1. 1.
    Fleming, H.W., Soner, H.M.: Controlled Markov Processes and Viscosity Solutions. Springer, Berlin (2006)zbMATHGoogle Scholar
  2. 2.
    Liptser, R.S., Shiryaev, A.N.: Statistics of Random Processes: I. General Theory. Springer, Berlin (2013)Google Scholar
  3. 3.
    Lungu, E.M., Øksendal, B.: Optimal harvesting from a population in a stochastic crowded environment. Math. Biosci. 145, 47–75 (1997)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Øksendal, B.: Stochastic Differential Equations. Springer, Berlin (2003)CrossRefGoogle Scholar
  5. 5.
    Oleinik, O.A., Radkevic, E.V.: Second-Order Equations with Nonnegative Characteristic Form. Springer, Berlin (2006)Google Scholar
  6. 6.
    Valkov, R.: Convergence of a finite volume element method for a generalized Black-Scholes equation transformed on finite interval. Numer. Algorithms 68, 61–80 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, J., Forsyth, P.A.: Maximal use of central differencing for Hamilton-Jacobi-Bellman PDEs in finance. SIAM J. Numer. Anal. 46, 1580–1501 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Yoshioka, H., Yaegashi, Y.: Optimization model to start harvesting in stochastic aquaculture system. Appl. Stoch. Model. Bus. Ind. 33, 476–493 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Yoshioka, H., Yaegashi, Y.: Mathematical analysis for management of released fish. Optimal Control Appl. Methods 39, 1141–1146 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Hidekazu Yoshioka
    • 1
    Email author
  • Yuta Yaegashi
    • 2
  • Yumi Yoshioka
    • 3
  • Kentaro Tsugihashi
    • 4
  1. 1.Graduate School of Natural Science and TechnologyShimane UniversityMatsueJapan
  2. 2.Graduate School of AgricultureKyoto UniversitySakyo-kuJapan
  3. 3.Faculty of AgricultureTottori UniversityTottoriJapan
  4. 4.Graduate School of Life and Environmental ScienceShimane UniversityMatsueJapan

Personalised recommendations