Efficient rare-event simulation for multiple jump events in regularly varying random walks and compound Poisson processes

Bohan Chen, Jose Blanchet, Chang Han Rhee, Bert Zwart

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4 Citations (Scopus)
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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 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.

Original languageEnglish
Pages (from-to)919-942
Number of pages24
JournalMathematics of Operations Research
Volume44
Issue number3
DOIs
Publication statusPublished - 2019

Bibliographical note

Funding Information:
Funding: The work of B. Chen, C-H. Rhee, and B. Zwart was supported by the Netherlands Orga-nisation for Scientific Research [Vici Grant 639.033.413]. The work of J. Blanchet was supported by the National Science Foundation [Grants 132055, 1538217, 1820942] and the Defense Advanced Research Projects Agency [Grant N660011824028].

Publisher Copyright:
© 2019 INFORMS

Keywords

  • Compound Poisson processes
  • Large deviations results
  • Principle of multiple big jumps
  • Random walks
  • Rare-event simulation
  • Regularly varying distribution
  • Strong efficiency

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