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MODERATE DEVIATION PRINCIPLES FOR IMPORTANCE SAMPLING ESTIMATORS OF RISK MEASURES
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics. Brown Univ, USA.ORCID iD: 0000-0001-8702-2293
2017 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 54, no 2, 490-506 p.Article in journal (Refereed) Published
Abstract [en]

Importance sampling has become an important tool for the computation of extreme quantiles and tail-based risk measures. For estimation of such nonlinear functionals of the underlying distribution, the standard efficiency analysis is not necessarily applicable. In this paper we therefore study importance sampling algorithms by considering moderate deviations of the associated weighted empirical processes. Using a delta method for large deviations, combined with classical large deviation techniques, the moderate deviation principle is obtained for importance sampling estimators of two of the most common risk measures: value at risk and expected shortfall.

Place, publisher, year, edition, pages
Cambridge University Press, 2017. Vol. 54, no 2, 490-506 p.
Keyword [en]
Large deviation, moderate deviation, risk measure, empirical process, asymptotics, importance sampling, Monte Carlo
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-211029DOI: 10.1017/jpr.2017.13ISI: 000404012100010Scopus ID: 2-s2.0-85021080099OAI: oai:DiVA.org:kth-211029DiVA: diva2:1121670
Note

QC 20170712

Available from: 2017-07-12 Created: 2017-07-12 Last updated: 2017-07-12Bibliographically approved

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