Optimal Exploitation of a Resource with Stochastic Population Dynamics and Delayed Renewal
| Autor: | Idris Kharroubi, Vathana Ly Vath, Thomas Lim |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Mathematical optimization
Optimization problem viscosity solutions execution delay Population 01 natural sciences optimal harvesting Stochastic differential equation Resource (project management) renewable resource Order (exchange) Bellman equation Market price FOS: Mathematics 0101 mathematics states constraints education Mathematics - Optimization and Control Mathematics education.field_of_study Applied Mathematics 010102 general mathematics 010101 applied mathematics Dynamic programming Optimization and Control (math.OC) [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Analysis impulse control |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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