Haezendonck–Goovaerts risk measures is a recently introduced class of risk measures which includes, as its minimal member, the Tail Value-at-Risk (T-VaR)—T-VaR arguably the most popular risk measure in global insurance regulation. In applications often one has to estimate the risk measure...

In a 2-dimensional space, Fréchet–Hoeffding upper and lower bounds define comonotonicity and countermonotonicity, respectively. Similarly, in the multidimensional case, comonotonicity can be defined using the Fréchet–Hoeffding upper bound. However, since the multidimensional...

The Conditional Tail Expectation (CTE) is gaining an increasing level of attention as a measure of risk. It is known that nonparametric unbiased estimators of the CTE do not exist, and that , the empirical [alpha]-level CTE (the average of the n(1-[alpha]) largest order statistics in a random...