Fitted Finite Volume Method of Three Transboundary Pollution in Three Gorges Reservoir Area of Chongqing City with Emission Permits Trading by Cooperative Stochastic Differential Game (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we present a stochastic differential game to model the three transboundary industrial pollution problems in Three Gorges Reservoir Area of Chongqing City with emission permits trading. The process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion. We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman equations satisfied by the value functions for the cooperative games, and then propose a fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by an empirical study for Wanzhou District, Kaizhou District, and Yunyang County in  Chongqing City.