With the decision made to act upon climate change, the remaining question is: "How?". Economic theory suggests that the most efficient method is by means of market-based policies. These policies are often designed based on Integrated Assessment Models like DICE, which is the subject of this thesis. Integrating uncertainty into this model has been the aim of the thesis. The stochastic version of DICE, EICE, showed to be sensitive to the distribution of climate uncertainty, but results were less explicit then expected. Overall, the conclusion is that both modest and more strict mitigation policies can be justified based on EICE.