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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: 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.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.


Related in: MedlinePlus

The effects of E10 on the cooperative game.
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pone.0138641.g015: The effects of E10 on the cooperative game.

Mentions: From Figs 14 and 17, we know that the two regions’ initial quotas only influence their own net revenues, respectively, in the noncooperative game and without any changes in emission levels. Moreover, the more the initial quotas are, the greater the net revenues are, which is similar to the cooperative cases presented in Figs 15 and 18. In the cooperative game, the addition in either region’s initial quota can all increase the joint net revenue. Similarly, this is due to the sharing of two regions’ information and resources in the cooperative game.


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 cooperative game.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0138641.g015: The effects of E10 on the cooperative game.
Mentions: From Figs 14 and 17, we know that the two regions’ initial quotas only influence their own net revenues, respectively, in the noncooperative game and without any changes in emission levels. Moreover, the more the initial quotas are, the greater the net revenues are, which is similar to the cooperative cases presented in Figs 15 and 18. In the cooperative game, the addition in either region’s initial quota can all increase the joint net revenue. Similarly, this is due to the sharing of two regions’ information and resources in the cooperative game.

Bottom Line: 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.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.


Related in: MedlinePlus