Minimization of carbon abatement cost: Modeling, analysis and simulation

In this paper, we consider a problem of minimizing the carbon abatement cost of a country. Two models are built within the stochastic optimal control framework based on two types of abatement policies. The corresponding HJB equations are deduced, and the existence and uniqueness of their classical solutions are established by PDE methods. Using parameters in the models obtained from real data, we carried out numerical simulations via semi-implicit method. Then we discussed the properties of the optimal policies and minimal costs. Our results suggest that a country needs to keep a relatively low economy and population growth rate and keep a stable economy in order to reduce the total carbon abatement cost. In the long run, it's better for a country to seek for more efficient carbon abatement techniques and an environmentally friendly way of economic development.