In the analysis of the risk associated to rare events that may lead to catastrophic consequences with large uncertainty, it is questionable that the knowledge and information available for the analysis can be reflected properly by probabilities. Approaches other than purely probabilistic have been suggested, for example using interval probabilities, possibilistic measures, or qualitative methods. In the present paper, we look into the problem and identify a number of issues which are foundational for its treatment. The foundational issues addressed reflect on the position that "probability is perfect" and take into open consideration the need for an extended framework for risk assessment that reflects the separation that practically exists between analyst and decision maker.

The concept of emerging risk has gained increasing attention in recent years. The term has an intuitive appeal and meaning but a consistent and agreed definition is missing. We perform an in-depth analysis of this concept, in particular its relation to black swan type of events, and show that these can be considered meaningful and complementary concepts by relating emerging risk to known unknowns and black swans to unknown knowns, unknown unknowns and a subset of known knowns. The former is consistent with saying that we face emerging risk related to an activity when the background knowledge is weak but contains indications/justified beliefs that a new type of event (new in the context of that activity) could occur in the future and potentially have severe consequences to something humans value. The weak background knowledge among other things results in difficulty specifying consequences and possibly also in fully specifying the event itself; i.e. in difficulty specifying scenarios.Here knowledge becomes the key concept for both emerging risk and black swan type of events, allowing for taking into consideration time dynamics since knowledge develops over time. Some implications of our findings in terms of risk assessment and risk management are pointed out.

Expert knowledge is an important source of input to risk analysis. In practice, experts might be reluctant to characterize their knowledge and the related (epistemic) uncertainty using precise probabilities. The theory of possibility allows for imprecision in probability assignments. The associated possibilistic representation of epistemic uncertainty can be combined with, and transformed into, a probabilistic representation; in this article, we show this with reference to a simple fault tree analysis. We apply an integrated (hybrid) probabilistic-possibilistic computational framework for the joint propagation of the epistemic uncertainty on the values of the (limiting relative frequency) probabilities of the basic events of the fault tree, and we use possibility-probability (probability-possibility) transformations for propagating the epistemic uncertainty within purely probabilistic and possibilistic settings. The results of the different approaches (hybrid, probabilistic, and possibilistic) are compared with respect to the representation of uncertainty about the top event (limiting relative frequency) probability. Both the rationale underpinning the approaches and the computational efforts they require are critically examined. We conclude that the approaches relevant in a given setting depend on the purpose of the risk analysis, and that further research is required to make the possibilistic approaches operational in a risk analysis context.

In safety settings, understood as situations involving the potential occurrence of unintentional events, it is common to define risk as a combination of consequences and associated probabilities or associated uncertainties. On the other hand, in security settings, understood as situations involving the potential occurrence of intentional malicious events, risk is commonly defined as the triplet asset/value, threat and vulnerability. One motivation often mentioned for the latter is that probability is considered inappropriate for intentional acts. In this article, we argue that it is unsuitable and unnecessary to define risk differently in these two settings. We show that risk, defined as the combination of future consequences and associated uncertainties, can be seen as compatible with the triplet definition of security risk. It also excludes probability from the definition of risk but explicitly includes uncertainty, which is more fundamental and present regardless of the type of events involved. The value dimension is integrated with the consequences as these are with respect to something that humans value. The purpose of the article is to contribute to a consolidation of the safety and security risk management fields at the fundamental level.

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Risk analysis as a field and discipline is about concepts, principles, approaches, methods, and models for understanding, assessing, communicating, managing, and governing risk. The foundation of this field and discipline has been subject to continuous discussion since its origin some 40 years ago with the establishment of the Society for Risk Analysis and the Risk Analysis journal. This article provides a perspective on critical foundational challenges that this field and discipline faces today, for risk analysis to develop and have societal impact. Topics discussed include fundamental questions important for defining the risk field, discipline, and science; the multidisciplinary and interdisciplinary features of risk analysis; the interactions and dependencies with other sciences; terminology and fundamental principles; and current developments and trends, such as the use of artificial intelligence.