Jose Blanchet and Chenxin Li. 2011. Efficient rare event simulation for heavy-tailed compound sums. ACM Trans. Model. Comput. Simul. 21, 2, Article 9 (February 2011), 23 pages. https://doi.org/10.1145/1899396.1899397
Abstract
We develop an efficient importance sampling algorithm for estimating the tail distribution of heavy-tailed compound sums, that is, random variables of the form SM=Z1+…+ZM where the Zi's are independently and identically distributed (i.i.d.) random variables in R and M is a nonnegative, integer-valued random variable independent of the Zi's. We construct the first estimator that can be rigorously shown to be strongly efficient only under the assumption that the Zi's are subexponential and M is light-tailed. Our estimator is based on state-dependent importance sampling and we use Lyapunov-type inequalities to control its second moment. The performance of our estimator is empirically illustrated in various instances involving popular heavy-tailed models.
Authors
Jose Blanchet, Chenxin Li
Publication date
2011/2/18
Journal
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Volume
21
Issue
2
Pages
1-23
Publisher
ACM
