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

被引：0

作者：

Gaigi, M'hamed ^{[1
]}

Kharroubi, Idris ^{[2
]}

Lim, Thomas ^{[3
]}

机构：

[1] Univ Tunis El Manar, Ecole Natl Ingenieurs Tunis LAMSIN, Tunis 2092, Tunisia

[2] Univ Paris, Sorbonne Univ, CNRS, Lab Probabil Stat & Modelisat LPSM, F-75005 Paris, France

[3] Ecole Natl Super Informat Ind & Entreprise, Lab Math & Modelisat Evry, CNRS UMR 8071, F-91037 Evry, France

来源：

MATHEMATICS | 2020年 / 8卷 / 11期

关键词：

impulse control; natural resource; optimal harvesting; execution delay; viscosity solutions; state constraints; IMPULSE CONTROL; LIQUIDITY RISK; INVESTMENT;

D O I：

10.3390/math8112053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1 / 25

页数：25

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