Greenhouse gas policies confront the trade-off between the costs of reducing emissions and the benefits of avoided climate change. The risk of uncertain and potentially irreversible catastrophes is an important issue related to the latter, and one that has not yet been well incorporated into economic models for climate change policy analysis. This paper demonstrates a multistage stochastic programming framework for catastrophe modeling with endogenous uncertainty, applied to a benchmark integrated assessment model. This study moves beyond recent catastrophe or tipping point studies with arbitrary risk, instead investigating the specific threat of the uncertain collapse of the West Antarctic Ice Sheet (WAIS), characterized in accordance with recent expert elicitations, empirical results, and physical relationships. The stochastic DICE-WAIS model introduced here informs risk management strategies that balance uncertain future climate change impacts with the costs of mitigation investments today. This work finds that accounting for the consequences of the possible WAIS collapse in a stochastic setting with endogenous uncertainty leads to more stringent climate policy recommendations (increasing the CO2 control rate by an additional 4% of global emissions and raising the social cost of carbon by $10), reflecting the need to hedge against uncertainties with downside risk as well as pursue precautionary mitigation.