Rare events probability estimation of sums of heavy-tailed random variables: an alternative approach

Estimation of rare event probabilities of sums of heavy-tailed random variables is one of the issues of the recent simulation literature which has not yet found a completely satisfactory solution achieving in a general setting a bounded relative error. Several methods have been proposed in literature mainly based on conditional Monte Carlo simulation.We propose an alternative estimator extending the approach introduced in Arima et al (2010) for computing the rare event probability of a single random variable. The original estimator actually relies on an importance sampling scheme based on a reflection mapping of the original variable such that the event whose probability we aim at estimating lies in a region which is not so rare for the reflected variable. We prove by simulations that the proposed estimator can achieve bounded relative error and compare its performance with existing ones.