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Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game

Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits pri...

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Detalles Bibliográficos
Autores principales: Chang, Shuhua, Wang, Xinyu, Wang, Zheng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4581629/
https://www.ncbi.nlm.nih.gov/pubmed/26402322
http://dx.doi.org/10.1371/journal.pone.0138641
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author Chang, Shuhua
Wang, Xinyu
Wang, Zheng
author_facet Chang, Shuhua
Wang, Xinyu
Wang, Zheng
author_sort Chang, Shuhua
collection PubMed
description Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion (GBM). We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions for the cooperative and the noncooperative games, respectively, and then propose a so-called fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by the numerical experiments. The two regions’ cooperative and noncooperative optimal emission paths, which maximize the regions’ discounted streams of the net revenues, together with the value functions, are obtained. Additionally, we can also obtain the threshold conditions for the two regions to decide whether they cooperate or not in different cases. The effects of parameters in the established model on the results have been also examined. All the results demonstrate that the stochastic emission permits prices can motivate the players to make more flexible strategic decisions in the games.
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spelling pubmed-45816292015-10-01 Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game Chang, Shuhua Wang, Xinyu Wang, Zheng PLoS One Research Article Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion (GBM). We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions for the cooperative and the noncooperative games, respectively, and then propose a so-called fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by the numerical experiments. The two regions’ cooperative and noncooperative optimal emission paths, which maximize the regions’ discounted streams of the net revenues, together with the value functions, are obtained. Additionally, we can also obtain the threshold conditions for the two regions to decide whether they cooperate or not in different cases. The effects of parameters in the established model on the results have been also examined. All the results demonstrate that the stochastic emission permits prices can motivate the players to make more flexible strategic decisions in the games. Public Library of Science 2015-09-24 /pmc/articles/PMC4581629/ /pubmed/26402322 http://dx.doi.org/10.1371/journal.pone.0138641 Text en © 2015 Chang et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Chang, Shuhua
Wang, Xinyu
Wang, Zheng
Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game
title Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game
title_full Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game
title_fullStr Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game
title_full_unstemmed Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game
title_short Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game
title_sort modeling and computation of transboundary industrial pollution with emission permits trading by stochastic differential game
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4581629/
https://www.ncbi.nlm.nih.gov/pubmed/26402322
http://dx.doi.org/10.1371/journal.pone.0138641
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