Climate Change features a variety of uncertainties. Besides the physical implications, e.g. increased frequency and severity of storms, floods, draughts and extreme weather events, there are many economically relevant uncertainties in terms of political, social and regulatory reactions. In particular, the quantification of climate risk in a probabilistic framework carries high uncertainties for probabilities of future developments (scenarios). As a consequence, quantitative approaches are highly controversial in the academic and in particular in the public discussion. So far a systematic approach to the various degrees of uncertainty (ambiguity) is missing. In this article, we we use a decision-theoretic approach motivated from the asset pricing literature to provide a systematic classification of the various effects of uncertainty and apply it to questions arising in the context of climate policy. In particular, we find that it is necessary to use a separation of risk and time preferences (in the spirit of the approach of Epstein-Zin, 1989) as well as an explicit inclusion of the aversion towards ambiguity. We illustrate our approach by discussing the social discount factor and a two-period (generation) stock pollutant model.