We investigate the importance of explicitly accounting for uncertainty in the determination of optimal global climate policy. We demonstrate that the marginal risk premium determines the importance of adapting the optimal policy to uncertainty. Common integrated assessment models (IAM) of climate change suggest uncertainty has little effect because the marginal risk premium in these models is small. A rigorous investigation of the marginal risk premium and the marginal functional relationships within IAMs allows understanding the non-significance of (thin-tailed) uncertainty as a result of compensating factors in the climate cause-effect chain.