Blanchet, J., & Liu, J. (2012). Efficient simulation and conditional functional limit theorems for ruinous heavy-tailed random walks. Stochastic Processes and Their Applications, 122(8), 2994-3031. https://doi.org/10.1016/j.spa.2012.05.001
Abstract
The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed random walks. Our changes of measures are parameterized by a family of distributions admitting a mixture form. We exploit our methodology to achieve two types of results. First, we construct Monte Carlo estimators that are strongly efficient (i.e. have bounded relative mean squared error as the event of interest becomes rare). These estimators are used to estimate both rare-event probabilities of interest and associated conditional expectations. We emphasize that our techniques allow us to control the expected termination time of the Monte Carlo algorithm even if the conditional expected stopping time (under the original distribution) given the event of interest is infinity–a situation that sometimes occurs in heavy-tailed settings. Second, the mixture family serves as a good Markovian …
Authors
Jose Blanchet, Jingchen Liu
Publication date
2012/8/1
Journal
Stochastic Processes and Their Applications
Volume
122
Issue
8
Pages
2994-3031
Publisher
North-Holland
