Insurers draw on sophisticated models for the probability distributions over losses associated with catastrophic events that are required to price insurance policies. But prevailing pricing methods don’t factor in the ambiguity around model-based projections that derive from the relative paucity of data about extreme events. I argue however that most current theories of decision making under ambiguity only partially support a solution to the challenge that insurance decision makers face and propose an alternative approach that allows for decision making that is responsive to both the evidential situation of the insurance decision maker and their attitude to ambiguity.