We consider the problem where a modeller conducts sensitivity analysis of a model consisting of random input factors, a corresponding random output of interest, and a baseline probability measure. The modeller seeks to understand how the model (the distribution of the input factors as well as...

The required solvency capital for a financial portfolio is typically given by a tail risk measure such as Value-at-Risk. Estimating the value of that risk measure from a limited, often small, sample of data gives rise to potential errors in the selection of the statistical model and the...

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decision maker is able to set the threshold at an appropriate level. This abstract situation applies for example to...

Actuarial research has aimed to tame uncertainty, typically by building on two premises: (a) the malleability of uncertainty to quantification and (b) the separability of quantitative modelling from decision principles. We argue that neither of the two premises holds true. The first ignores...