In this paper, based on the framework of the single-period model, we establish an optimal control model for the inheriting period which allows inter-phase banking and borrowing of allowances under the cap-and-trade system. By considering the abatement control policy and the initial auction amount of allowances, we optimize the problem in two steps. The two models can then be expressed using the Hamilton–Jacobi–Bellman (HJB) equations. In the framework of viscosity solution, we prove that the value functions in two models are the unique viscosity solutions of the corresponding HJB equations. Finally, we analyze the properties of optimal policy by referring to numerical results and a comparison of the two models is presented. Our results show that under the same circumstances, allowing inter-phase banking and borrowing of allowances indeed reduces the company’s abatement costs and has an incentive-based effect on the company’s emission reductions.

本文基于单期模型的框架，建立了限额交易制度下允许跨期存入和借用配额的继承期最优控制模型。通过考虑减排控制政策和配额的初始拍卖量，我们分两步优化问题。然后可以使用 Hamilton-Jacobi-Bellman (HJB) 方程来表示这两个模型。在粘度解的框架内，我们证明了两个模型中的值函数是对应的HJB方程的唯一粘度解。最后，我们通过参考数值结果分析了最优策略的特性，并给出了两种模型的比较。我们的结果表明，在相同的情况下，