In this article, we conduct a number of benefit–cost analyses to clarify whether the establishment of ragweed in Denmark should be prevented (pure prevention) or if the damage from this invasive species should be mitigated (pure mitigation). The main impact of the establishment of ragweed in Denmark would be a substantial increase in the number of allergy cases, which we use as a measure of the physical damage from this species. As valuation methods, we use both the cost-of-illness and benefit transfer methods to quantify the total gross benefits of these two policy actions. Based on the idea of an invasion function, we identify the total and average net benefits under both prevention and mitigation and find that all are significantly positive regardless of the valuation method. Therefore, both prevention and mitigation are beneficial policy actions, but the total and average net benefits under mitigation are larger than those under prevention in all the scenarios we consider. This finding implies that the former policy action is more beneficial. Despite this result, we propose that prevention, not mitigation, may be the proper policy because of information externalities, altruistic preferences, possible catastrophic events, and ethical considerations.