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Optimal management and valuation of a natural resource: the case of optimal harvesting

Published online by Cambridge University Press:  11 March 2022

M'hamed Gaïgi Open the ORCID record for M'hamed Gaïgi [Opens in a new window] ,
Idris Kharroubi  and
Thomas Lim
M'hamed Gaïgi
Affiliation:
ENIT-LAMSIN, Université de Tunis El Manar, Tunis, Tunisia. E-mail: mhamed.gaigi@enit.utm.tn
Idris Kharroubi
Affiliation:
LPSM, CNRS, UMR 8001, Sorbonne Université, Paris, France. E-mail: idris.kharroubi@upmc.fr
Thomas Lim
Affiliation:
LaMME, CNRS UMR 8071, ENSIIE, Évry, France. E-mail: lim@ensiie.fr
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Abstract

In this paper, we consider the problem of sustainable harvesting. We explain how the manager maximizes his/her profit according to the quantity of natural resource available in a harvesting area and under the constraint of penalties and fines when the quota is exceeded. We characterize the optimal values and some optimal strategies using a verification result. We then show by numerical examples that this optimal strategy is better than naive ones. Moreover, we define a level of fines which insures the double objective of the sustainable harvesting: a remaining quantity of available natural resource to insure its sustainability and an acceptable income for the manager.

Keywords

Optimal controlOptimal harvestingRenewable resourceStates constraintsVerification theorem
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 3 , July 2023 , pp. 674 - 694
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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