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Abstract: We derive necessary and sufficient conditions on the utility func-tion to avoid fragility of a cost-benefit analysis to distributional assumptions. We apply our results to economy-climate catastrophe. We specify a stochastic economy-climate model, adapting Nordhaus ’ deterministic economy-climate model by allowing for Weitzman-type stochasticity. We show that, under expected power utility, the model is fragile to heavy-tailed distributional assumptions and we solve our model for two cases with compatible pairs of utility functions and heavy-tailed distributional assumptions. We further de-velop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces robust optimal policies. JEL Classification: D61; D81; Q5