We explore variance reduction techniques for estimating rare-event probabilities
associated with products of random variables. While the associated random
variables might be light-tailed, their products can be heavy-tailed so their
estimation is often difficult. Moreover, since the distribution of a product of
random variables is seldom available in explicit form, then it is not always
possible to implement traditional methods in a straightforward way. In this
talk, we show how to adapt existing techniques for estimating the probabilities
of interest and we further analyse their asymptotic performance. We complement
our results with applications in risk.
This is joint work with Leonardo Rojas-Nandayapa and Thomas Taimre.