NDLI: Efficient rare event simulation for heavy-tailed compound sums

Content Provider	ACM Digital Library
Author	Blanchet, Jose Li, Chenxin
Copyright Year	2011
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 $S_{M}=Z_{1}+&cdots;+Z_{M}$ where the $Z_{i}'s$ are independently and identically distributed (i.i.d.) random variables in R and $\textit{M}$ is a nonnegative, integer-valued random variable independent of the $Z_{i}'s.$ We construct the first estimator that can be rigorously shown to be strongly efficient only under the assumption that the $Z_{i}'s$ are subexponential and $\textit{M}$ 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.
Starting Page	1
Ending Page	23
Page Count	23
File Format	PDF
ISSN	10493301
e-ISSN	15581195
DOI	10.1145/1899396.1899397
Volume Number	21
Issue Number	2
Journal	ACM Transactions on Modeling and Computer Simulation (TOMACS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-02-18
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lyapunov inequalities Rare events Compound sums Importance sampling Strong efficiency Subexponential tails
Content Type	Text
Resource Type	Article
Subject	Computer Science Applications Modeling and Simulation

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Efficient rare event simulation for heavy-tailed compound sums