The efficient simulation of rare events related to tail probabilities of functions of heavy-tailed random variables is a difficult but important problem in disciplines such as insurance, finance and telecommunications.  In the past few years a significative amount of attention has been devoted to this problem and a good number of interesting results have been produced. However, most of them are focused on sums of independent random variables. Therefore, our research is heavily focused on dependent random variables and more general functions than the sum alone.
 
In this talk I will show two new results suitable for a large number of models.  The first of them is a Conditional Monte Carlo algorithm for functions of log-elliptic random vectors which can be proved to be efficient assuming very mild conditions.  The second is an Importance Sampling algorithm which applies only for the tail probability of sums of random variables which can be shown to be efficient for a larger class of multivariate distributions.