Moderate deviations for importance sampling estimators of risk measures
AbstractImportance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a way to speed up computations. This paper considers moderate deviations for the weighted empirical process, the process analogue of the weighted empirical measure, arising in importance sampling. The moderate deviation principle is established as an extension of existing results. Using a delta method for large deviations established by Gao and Zhao (Ann. Statist., 2011) together with classical large deviation techniques, the moderate deviation principle for the weighted empirical process is extended to functionals of the weighted empirical process which correspond to risk measures. The main results are moderate deviation principles for importance sampling estimators of the quantile function of a distribution and Expected Shortfall.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1306.6588.
Date of creation: Jun 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-07-05 (All new papers)
- NEP-ECM-2013-07-05 (Econometrics)
- NEP-RMG-2013-07-05 (Risk Management)
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- Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value-at-Risk with Heavy-Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(3), pages 239-269.
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