Rare events simulation for heavy tailed distributions

S. Asmussen, K. Binswanger and B. Höjgaard

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

ISSN 0281-1944

This paper studies rare events simulation for the heavy-tailed case, where some of the underlying distributions  fail to have the exponential moments required for the standard algorithms for the light-tailed case. Several counterexamples are given to indicate that in the heavy-tailed case, there are severe problems with the approach of developing limit results for the conditional distribution given the rare event and use this as basis for importance sampling. On the positive side, two algorithms having almost relative bounded error are presented, one based upon order statistics and the other upon a different importance sampling idea.