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The purpose of this article is to discuss the role of quantitative risk assessments for characterizing risk and uncertainty and delineating appropriate risk management options. Our main concern is situations (risk problems) with large potential consequences, large uncertainties, and/or ambiguities (related to the relevance, meaning, and implications of the decision basis; or related to the values to be protected and the priorities to be made), in particular terrorism risk. We look into the scientific basis of the quantitative risk assessments and the boundaries of the assessments in such a context. Based on a risk perspective that defines risk as uncertainty about and severity of the consequences (or outcomes) of an activity with respect to something that humans value we advocate a broad risk assessment approach characterizing uncertainties beyond probabilities and expected values. Key features of this approach are qualitative uncertainty assessment and scenario building instruments.
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