Tolerance intervals for quantiles of bivariate risks and risk measurement

This paper considers joint distributions of order statistics for risk variables and their concomitants for actuarial risk analysis under dependence. With this purpose, bivariate integral transformations are performed and some examples are presented using copulas, the FGM copulas in particular. Quantiles of the distributions concerned are discussed and their tolerance intervals are constructed. Risk measures such as VaR in the set up of the tolerance intervals are included in the discussions.