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

Chang S, Wang X, Wang Z - PLoS ONE (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China.

ABSTRACT
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.

No MeSH data available.


The effects of E10 on the optimal decision boundary.
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pone.0138641.g016: The effects of E10 on the optimal decision boundary.

Mentions: Figs 16 and 19, where we fix α = 0.6 as above, show the effects of two regions’ initial quotas on the optimal decision boundary. We can see from the two figures that the initial quotas, especially the disadvantaged region 2’s, have limited influence on the optimal decision boundary. The reason for the little influence of E10 is that region 1 may do not want to share the more initial quotas with region 2, and prefers not to cooperate, which is the feature of Fig 16.


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

Chang S, Wang X, Wang Z - PLoS ONE (2015)

The effects of E10 on the optimal decision boundary.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4581629&req=5

pone.0138641.g016: The effects of E10 on the optimal decision boundary.
Mentions: Figs 16 and 19, where we fix α = 0.6 as above, show the effects of two regions’ initial quotas on the optimal decision boundary. We can see from the two figures that the initial quotas, especially the disadvantaged region 2’s, have limited influence on the optimal decision boundary. The reason for the little influence of E10 is that region 1 may do not want to share the more initial quotas with region 2, and prefers not to cooperate, which is the feature of Fig 16.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China.

ABSTRACT
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.

No MeSH data available.