Efficient rare event simulation for heavy-tailed systems via cross entropy

The cross entropy method is an iterative technique that is used to obtain a low-variance importance sampling (IS) distribution from a given parametric family, which must satisfy two properties. First, subsequent iterations of the parameters must be easily computable and, second, the family should approximate the zero-variance IS distribution. We obtain parametric families for which these two properties are satisfied for a large class of heavy-tailed systems. Our estimators are shown to be strongly efficient in these settings.