排污权交易机制下跨界污染微分博弈模型的高效拟合有限体积方法

本项目拟研究建立以生产量、交易量以及能源技术投资为控制变量，含有排污权存储功能与能源效率变量的跨界污染微分博弈模型，并拟利用随机最优控制理论，将问题转化为等价的HJB偏微分方程组来定量地刻画排污权交易机制下的排放水平，以及排污权存储功能对博弈双方的收益、能源效率和污染物存量的影响。发展此问题中HJB方程组的拟合有限体积方法，建立算法的稳定性、单调性及收敛性理论，并给出相应问题拟合有限体积方法的超收敛结果。

In this project, by means of the control variables of the production, trading volume, and investment on energy technology, a differential game model for the transboundary pollution game with emission permits trading, banking, and energy efficiency is established. A equivalent Hamilton-Jacobi-Bellman system of partial differential equations is derived by using stochastic optimal control theory to describe quantitatively the emission level and the effects of banking on the players' profit, energy efficiency, as well as pollution stock under emission permits trading scheme. To solve the Hamilton-Jacobi-Bellman system of partial differential equations, a fitted finite volume method is proposed. The stability, monotonicity, convergence analysis, as well as the superconvergence are developed.