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

• 成果类型: Article
• 署名作者: Chen, Bohan; Blanchet, Jose; Rhee, Chang-Han; Zwart, Bert
• 署名单位: Stanford University; Northwestern University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0950
• 发表日期: 2019
• 页码: 919-942
• 关键词: probabilities; RISK

摘要

We propose a class of strongly efficient ram-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.