Rare-event probability estimation with conditional Monte Carlo

Chan, JCC; Kroese, DP

Rare-event probability estimation with conditional Monte Carlo

Chan, JCC

Kroese, DP

Permalink

Publication Type:: Journal Article
Citation:: Annals of Operations Research, 2011, 189 (1), pp. 43 - 61
Issue Date:: 2011-09-01

Closed Access

	Filename	Description	Size
	10.1007_s10479-009-0539-y.pdf	Published Version	642.25 kB	Adobe PDF	View/Open

Copyright Clearance Process

Recently Added
In Progress
Closed Access

This item is closed access and not available.

Full metadata record

Field	Value	Language
dc.contributor.author	Chan, JCC https://orcid.org/0000-0003-3632-128X	en_US
dc.contributor.author	Kroese, DP	en_US
dc.date.issued	2011-09-01	en_US
dc.identifier.citation	Annals of Operations Research, 2011, 189 (1), pp. 43 - 61	en_US
dc.identifier.issn	0254-5330	en_US
dc.identifier.uri	http://hdl.handle.net/10453/116124
dc.description.abstract	Estimation of rare-event probabilities in high-dimensional settings via importance sampling is a difficult problem due to the degeneracy of the likelihood ratio. In fact, it is generally recommended that Monte Carlo estimators involving likelihood ratios should not be used in such settings. In view of this, we develop efficient algorithms based on conditional Monte Carlo to estimate rare-event probabilities in situations where the degeneracy problem is expected to be severe. By utilizing an asymptotic description of how the rare event occurs, we derive algorithms that involve generating random variables only from the nominal distributions, thus avoiding any likelihood ratio. We consider two settings that occur frequently in applied probability: systems involving bottleneck elements and models involving heavy-tailed random variables. We first consider the problem of estimating ℙ(X1+· · ·+Xn>γ), where X1,...,Xn are independent but not identically distributed (ind) heavy-tailed random variables. Guided by insights obtained from this model, we then study a variety of more general settings. Specifically, we consider a complex bridge network and a generalization of the widely popular normal copula model used in managing portfolio credit risk, both of which involve hundreds of random variables. We show that the same conditioning idea, guided by an asymptotic description of the way in which the rare event happens, can be used to derive estimators that outperform existing ones. © 2009 Springer Science+Business Media, LLC.	en_US
dc.relation.ispartof	Annals of Operations Research	en_US
dc.relation.isbasedon	10.1007/s10479-009-0539-y	en_US
dc.subject.classification	Operations Research	en_US
dc.title	Rare-event probability estimation with conditional Monte Carlo	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	189	en_US
utslib.for	010205 Financial Mathematics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	08 Information and Computing Sciences	en_US
utslib.for	15 Commerce, Management, Tourism and Services	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Economics Discipline
utslib.copyright.status	closed_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	189	en_US

Abstract:

Estimation of rare-event probabilities in high-dimensional settings via importance sampling is a difficult problem due to the degeneracy of the likelihood ratio. In fact, it is generally recommended that Monte Carlo estimators involving likelihood ratios should not be used in such settings. In view of this, we develop efficient algorithms based on conditional Monte Carlo to estimate rare-event probabilities in situations where the degeneracy problem is expected to be severe. By utilizing an asymptotic description of how the rare event occurs, we derive algorithms that involve generating random variables only from the nominal distributions, thus avoiding any likelihood ratio. We consider two settings that occur frequently in applied probability: systems involving bottleneck elements and models involving heavy-tailed random variables. We first consider the problem of estimating ℙ(X1+· · ·+Xn>γ), where X1,...,Xn are independent but not identically distributed (ind) heavy-tailed random variables. Guided by insights obtained from this model, we then study a variety of more general settings. Specifically, we consider a complex bridge network and a generalization of the widely popular normal copula model used in managing portfolio credit risk, both of which involve hundreds of random variables. We show that the same conditioning idea, guided by an asymptotic description of the way in which the rare event happens, can be used to derive estimators that outperform existing ones. © 2009 Springer Science+Business Media, LLC.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/116124