In this study, a stochastic control model is established for a country to formulate a carbon abatement policy to minimize the total carbon reduction costs. Under Merton's consumption framework, by considering carbon trading, carbon abatement and penalties in a synthetic manner, the model is converted into a two-dimensional Hamilton--Jacobi--Bellman equation. We rigorously prove the existence and uniqueness of its viscosity solution. We also present the numerical results and discuss the properties of the optimal carbon reduction policy and the minimum total costs.

中文翻译：

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碳减排与交易的最优控制模型

在本研究中，建立了一个随机控制模型，以制定一个国家的碳减排政策，以最大限度地降低碳减排总成本。在Merton的消费框架下，综合考虑碳交易、碳减排和惩罚，将模型转化为二维Hamilton--Jacobi--Bellman方程。我们严格证明了其粘度解的存在性和唯一性。我们还提供了数值结果并讨论了最佳碳减排政策和最小总成本的性质。