Abstract
The extreme value theory (EVT) can be used to predict rare events and is a popular means for estimating the value at risk (VaR) by extrapolating the tails of a distribution. The focus of the present study is on one of the EVT methods, peak–over–threshold (POT). In this approach the thresholds of a generalized Pareto distribution (GPD) are assigned based on a Hill plot with shape parameter \((\xi)\) for various exceedance levels, where \((\xi)\) is estimated by applying Hill’s estimator based on the optimized \(k\) of the order statistics. A new approach for selecting \(k\) via Hill’s estimator obtained by using a type 8 quantile function is presented herein. The threshold obtained is then used to compute the VaR and the expected shortfall (ES) for an event. An illustration of the efficacy of the new approach based on real data obtained from Danish fire loss insurance claims is also included.
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ACKNOWLEDGMENTS
The authors thank King Mongkut’s University of Technology North Bangkok and Kasetsart University. Further, the authors are grateful to the reviewers for suggestions of the manuscript.
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Boonradsamee, J., Jaroengeratikun, U. & Bodhisuwan, W. An Optimal Threshod Selection Approach for the Value at Risk of the Extreme Events. Lobachevskii J Math 43, 2397–2410 (2022). https://doi.org/10.1134/S1995080222120071
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DOI: https://doi.org/10.1134/S1995080222120071