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Optimal sustainable harvesting of populations in random environments

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  • Alvarez E., Luis H.R.
  • Hening, Alexandru

Abstract

We study the optimal sustainable harvesting of a population that lives in a random environment. The novelty of our setting is that we maximize the asymptotic harvesting yield, both in an expected value and almost sure sense, for a large class of harvesting strategies and unstructured population models. We prove under relatively weak assumptions that there exists a unique optimal harvesting strategy characterized by an optimal threshold below which the population is maintained at all times by utilizing a local time push-type policy. We also discuss, through Abelian limits, how our results are related to the optimal harvesting strategies when one maximizes the expected cumulative present value of the harvesting yield and establish a simple connection and ordering between the values and optimal boundaries. Finally, we explicitly characterize the optimal harvesting strategies in two different cases, one of which is the celebrated stochastic Verhulst Pearl logistic model of population growth.

Suggested Citation

  • Alvarez E., Luis H.R. & Hening, Alexandru, 2022. "Optimal sustainable harvesting of populations in random environments," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 678-698.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:678-698
    DOI: 10.1016/j.spa.2019.02.008
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    References listed on IDEAS

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    1. Alvarez, Luis H. R., 2000. "Singular stochastic control in the presence of a state-dependent yield structure," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 323-343, April.
    2. Andrew Jack & Mihail Zervos, 2006. "A singular control problem with an expected and a pathwise ergodic performance criterion," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-19, June.
    3. Helmes, Kurt L. & Stockbridge, Richard H., 2011. "Thinning and harvesting in stochastic forest models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 25-39, January.
    4. Dreze, Jean & Stern, Nicholas, 1987. "The theory of cost-benefit analysis," Handbook of Public Economics, in: A. J. Auerbach & M. Feldstein (ed.), Handbook of Public Economics, edition 1, volume 2, chapter 14, pages 909-989, Elsevier.
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    Cited by:

    1. Ky Q. Tran & Bich T. N. Le & George Yin, 2022. "Harvesting of a Stochastic Population Under a Mixed Regular-Singular Control Formulation," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1106-1132, December.
    2. Dianetti, Jodi & Ferrari, Giorgio & Tzouanas, Ioannis, 2023. "Ergodic Mean-Field Games of Singular Control with Regime-Switching (extended version)," Center for Mathematical Economics Working Papers 681, Center for Mathematical Economics, Bielefeld University.

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