  Risk management is particularly concerned with extreme events, but analysing
these events is often hindered by the scarcity of data, especially in a
multivariate context. This data scarcity complicates risk management efforts.
Various tools can assess the risk posed by extreme events, even under
extraordinary circumstances. This paper studies the evaluation of univariate
risk for a given risk factor using metrics that account for its asymptotic
dependence on other risk factors. Data availability is crucial, particularly
for extreme events where it is often limited by the nature of the phenomenon
itself, making estimation challenging. To address this issue, two
non-parametric simulation algorithms based on multivariate extreme theory are
developed. These algorithms aim to extend a sample of extremes jointly and
conditionally for asymptotically dependent variables using stochastic
simulation and multivariate Generalised Pareto Distributions. The approach is
illustrated with numerical analyses of both simulated and real data to assess
the accuracy of extreme risk metric estimations.
