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Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints

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  • M’hamed Gaïgi

    (Ecole Nationale d’Ingénieurs de Tunis-LAMSIN, Université de Tunis El Manar, Tunis 2092, Tunisie)

  • Idris Kharroubi

    (Sorbonne Université, Université de Paris, CNRS, Laboratoire de Probabilités, Statistiques et Modélisations (LPSM), 75005 Paris, France)

  • Thomas Lim

    (Ecole Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise, Laboratoire de Mathématiques et Modélisation d’Evry, CNRS UMR 8071, 91037 Evry, France)

Abstract

In this work, we study an optimization problem arising in the management of a natural resource over an infinite time horizon. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager is allowed to harvest the resource and sell it at a stochastic market price modeled by a geometric Brownian process. We assume that there are delay constraints imposed on the decisions of the manager. More precisely, starting harvesting order and selling order are executed after a delay. By using the dynamic programming approach, we characterize the value function as the unique solution to an original partial differential equation. We complete our study with some numerical illustrations.

Suggested Citation

  • M’hamed Gaïgi & Idris Kharroubi & Thomas Lim, 2020. "Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints," Mathematics, MDPI, vol. 8(11), pages 1-25, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2053-:d:446729
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    References listed on IDEAS

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