2019-05-23
Efficient rare-event simulation for multiple jump events in regularly varying random walks and compound Poisson processes
Publication
Publication
Mathematics of Operations Research , Volume 44 - Issue 3 p. 919- 942
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 queueing network. We illustrate the versatility of our approach with several applications that arise in the context of mathematical finance, actuarial science, and queueing theory.
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doi.org/10.1287/moor.2018.0950 | |
Mathematics of Operations Research | |
Rare events: Asymptotics, Algorithms, Applications | |
Chen, B., Blanchet, J., Rhee, C.-H., & Zwart, B. (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. doi:10.1287/moor.2018.0950 |