Climate economics has been criticized for ignoring uncertainty, catastrophic changes, and tipping points (Stern 2016). The present paper addresses these issues. We consider multiple climate shocks which are recurring, random, uninsurable, and potentially large. The associated damages and the hazard rate are endogenously driven by the stock of greenhouse gases. We provide closed-form solutions for the optimal climate policy and the growth rate of the economy. The optimal path is characterized by a constant growth rate of consumption and of the capital stock until a shock arrives, triggering a downward jump in both variables. The mitigation policy consists of a simple and intuitive rule which requires spending a constant fraction of output on emissions abatement. In a quantitative assessment we show that under favorable conditions the abatement expenditure represents 0.5% of output, equivalent to $37 per ton carbon. Under less favorable conditions with respect to abatement technology and damages, coupled with a relative risk aversion which exceeds unity, the abatement propensity increases to 2.9%, equivalent to $212 per ton carbon, and it jumps to a striking 10% in the pessimistic scenario involving severe shocks and a possible crossing of a tipping point.