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Nonparametric inference for VaR, CTE, and expectile with high-order precision. (English) Zbl 1426.91311

Summary: Value-at-risk and conditional tail expectation are the two most frequently applied risk measures in quantitative risk management. Recently expectile has also attracted much attention as a risk measure because of its elicitability property. This article establishes empirical likelihood-based estimation with high-order precision for these three risk measures. The superiority of the estimation is justified both in theory and via simulation studies. Extensive simulation studies confirm that our method significantly improves the coverage probabilities for interval estimation of the three risk measures, compared to three competing methods available in the literature.

MSC:

91G70 Statistical methods; risk measures
62P05 Applications of statistics to actuarial sciences and financial mathematics
62G05 Nonparametric estimation

Software:

emplik
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References:

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