The goal of this project is the quantitative analysis of carbon reduction policies, namely Carbon Tax and Cap and Trade. For each of these policies, an optimal control model will be formulated; for Carbon Tax, the tax rate will serve as the control, for Cap and Trade, the controls will include the amounts of freely allocated allowances and the timing of their auctioning. In addition, import tari s and green investment subsidies will be considered as possible controls for both policies. The models will be applied to the EU Cap and Trade system in order to predict its performance, explore possibilities of its optimization and compare it with a hypothetical carbon taxation.