Moderate deviation principles for importance sampling estimators of risk measures

P. Nyquist

Research output: Contribution to journalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)490-506
Number of pages17
JournalJournal of Applied Probability
Issue number2
Publication statusPublished - 1 Jun 2017
Externally publishedYes


  • asymptotics
  • empirical process
  • importance sampling
  • Large deviation
  • moderate deviation
  • Monte Carlo
  • risk measure


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