Bohan Chen, Jose Blanchet, Chang-Han Rhee, Bert Zwart (2019) Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes. Mathematics of Operations Research 44(3):919-942. https://doi.org/10.1287/moor.2018.0950

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Abstract

We propose a class of strongly efficient rare-event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges on a recently established heavy-tailed sample-path large deviations result. The new estimators are straightforward to implement and can be used to systematically evaluate the probability of a wide range of rare events with bounded relative error. They are “universal” in the sense that a single importance sampling scheme applies to a very general class of rare events that arise in heavy-tailed systems. In particular, our estimators can deal with rare events that are caused by multiple big jumps (therefore, beyond the usual principle of a single big jump) as well as multidimensional processes such as the buffer content process of a …

Authors
Bohan Chen, Jose Blanchet, Chang-Han Rhee, Bert Zwart
Publication date
2019/8
Journal
Mathematics of Operations Research
Volume
44
Issue
3
Pages
919-942
Publisher
INFORMS