Optimal Exploitation of a Resource with Stochastic Population Dynamics and Delayed Renewal
Lim, Thomas; Kharroubi, Idris; Ly-Vath, Vathana (2018), Optimal Exploitation of a Resource with Stochastic Population Dynamics and Delayed Renewal. https://basepub.dauphine.fr/handle/123456789/17974
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01835011
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
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Laboratoire de Mathématiques et Modélisation d'Evry [LaMME]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 / Keywordsstates constraints; viscosity solutions; execution delay; impulse control; renewable resource; optimal harvesting
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