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

M’hamed Gaïgi, Idris Kharroubi and Thomas Lim
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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

Mathematics, 2020, vol. 8, issue 11, 1-25

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.

Keywords: impulse control; natural resource; optimal harvesting; execution delay; viscosity solutions; state constraints (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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