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

Xingyu Wang; Chang-Han Rhee

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arXiv · 2007.08080

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

Xingyu Wang·Chang-Han Rhee

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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.

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BibTeX RIS

Xingyu Wang, Chang-Han Rhee. 2020-07-16. Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying L\'evy Processes with Infinite Activities. https://arxiv.org/abs/2007.08080

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