Climate policy is fundamentally about managing risk. Most prominently, there is uncertainty about the sensitivity of the climate response to increased greenhouse gas (GHG) concentrations and about the impacts to society of a changing climate and our willingness to pay to avoid them. To understand the implications of these climate risks for mitigation decisions, a stochastic cost-benefit modeling framework is necessary. In this study, we use a new stochastic programming version of the MERGE integrated assessment model (IAM) to explore optimal hedging paths under uncertainty about both climate sensitivity and the damage function. Our results illustrate how the near-term mitigation strategy could effectively hedge against a potential risk characterization. More generally, our modeling framework provides a tool for communicating the implications of alternative assumptions about long-term climate risks for policy decisions today.