English

Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying L\'evy Processes with Infinite Activities

Probability 2020-07-17 v1

Abstract

In this paper we address the problem of rare-event simulation for heavy-tailed L\'evy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for heavy-tailed L\'evy processes, stick-breaking approximation of extrema of L\'evy processes, and the randomized debiasing Monte Carlo scheme. The proposed importance sampling algorithm can be applied to a broad class of L\'evy processes and exhibits significant improvements in efficiency when compared to crude Monte-Carlo method in our numerical experiments.

Keywords

Cite

@article{arxiv.2007.08080,
  title  = {Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying L\'evy Processes with Infinite Activities},
  author = {Xingyu Wang and Chang-Han Rhee},
  journal= {arXiv preprint arXiv:2007.08080},
  year   = {2020}
}
R2 v1 2026-06-23T17:09:24.430Z