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Optimal Exploitation of a Resource with Stochastic Population Dynamics and Delayed Renewal

Kharroubi, Idris; Lim, Thomas; Ly-Vath, Vathana (2019), Optimal Exploitation of a Resource with Stochastic Population Dynamics and Delayed Renewal, Journal of Mathematical Analysis and Applications, 477, 1, p. 627-656. 10.1016/j.jmaa.2019.04.052

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Journal of Mathematical Analysis and Applications
Volume
477
Number
1
Publisher
Elsevier
Pages
627-656
Publication identifier
10.1016/j.jmaa.2019.04.052
Metadata
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Author(s)
Kharroubi, Idris
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
Lim, Thomas
Laboratoire de Mathématiques et Modélisation d'Evry [LaMME]
Ly-Vath, Vathana
Abstract (EN)
In this work, we study the optimization problem of a renewable resource in finite time. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager may harvest partially the resource at any time and sell it at a stochastic market price. She may equally decide to renew part of the resource but uniquely at deterministic times. However, we realistically assume that there is a delay in the renewing order. By using the dynamic programming theory, we may obtain the PDE characterization of our value function. To complete our study, we give an algorithm to compute the value function and optimal strategy. Some numerical illustrations will be equally provided.
Subjects / Keywords
states constraints; viscosity solutions; execution delay; impulse control; renewable resource; optimal harvesting

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