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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 α on the optimal decision boundary.
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pone.0138641.g004: The effects of α on the optimal decision boundary.

Mentions: Although the increasing α results in more joint net revenues, it is not always true for any pollution stock P in the case that the joint value function VC is larger than the sum of the net revenues VN1 and VN2 in the noncooperative game. Fig 4 shows the boundaries at which the two players should change their decisions from the cooperation to the noncooperation for different α at time t = 0. Similar to the optimal exercise boundaries in American options, the curve, which can be called “optimal decision boundary”, divides the domain Ω = (Pmin,Pmax) × (Smin,Smax) into the cooperative region and the noncooperative region. In the cooperative region, the optimal cooperative net revenue is always higher than the sum of the noncooperative net revenues, and in the noncooperative region, the sum of the noncooperative net revenues is larger than the cooperative one, and on the optimal decision boundary, they are the same.


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 α on the optimal decision boundary.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0138641.g004: The effects of α on the optimal decision boundary.
Mentions: Although the increasing α results in more joint net revenues, it is not always true for any pollution stock P in the case that the joint value function VC is larger than the sum of the net revenues VN1 and VN2 in the noncooperative game. Fig 4 shows the boundaries at which the two players should change their decisions from the cooperation to the noncooperation for different α at time t = 0. Similar to the optimal exercise boundaries in American options, the curve, which can be called “optimal decision boundary”, divides the domain Ω = (Pmin,Pmax) × (Smin,Smax) into the cooperative region and the noncooperative region. In the cooperative region, the optimal cooperative net revenue is always higher than the sum of the noncooperative net revenues, and in the noncooperative region, the sum of the noncooperative net revenues is larger than the cooperative one, and on the optimal decision boundary, they are the same.

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