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We propose a class of strongly efficient rare event simulation estimators forrandom walks and compound Poisson processes with a regularly varyingincrement/jump-size distribution in a general large deviations regime. Ourestimator is based on an importance sampling strategy that hinges on theheavy-tailed sample path large deviations result recently established in Rhee,Blanchet, and Zwart (2016). The new estimators are straightforward to implementand can be used to systematically evaluate the probability of a wide range ofrare events with bounded relative error. They are "universal" in the sense thata single importance sampling scheme applies to a very general class of rareevents that arise in heavy-tailed systems. In particular, our estimators candeal with rare events that are caused by multiple big jumps (therefore, beyondthe usual principle of a single big jump) as well as multidimensional processessuch as the buffer content process of a queueing network. We illustrate theversatility of our approach with several applications that arise in the contextof mathematical finance, actuarial science, and queueing theory.

Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes