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Journal Articles Mathematics Year : 2020

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

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. View Full-Text
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hal-03065959 , version 1 (15-12-2020)

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M’hamed Gaïgi, Idris Kharroubi, Thomas Lim. Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints. Mathematics , 2020, 8 (11), pp.2053. ⟨10.3390/math8112053⟩. ⟨hal-03065959⟩
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