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 this paper, we investigate the asymptotic behavior of the portfolio diversification ratio based on Value-at-Risk (quantile) under dependence uncertainty, which we refer to as "worst-case diversification limit." We show that the worst-case diversification limit is equal to the upper limit of...

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...