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.

Additional Metadata
Keywords Compound Poisson processes, Large deviations results, Principle of multiple big jumps, Random walks, Rare-event simulation, Regularly varying distribution, Strong efficiency
Persistent URL dx.doi.org/10.1287/moor.2018.0950
Journal Mathematics of Operations Research
Citation
Chen, B, Blanchet, J, Rhee, C.H, & Zwart, A.P. (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