Abstract
Using a distortion risk premium principle, we consider estimation of the reinsurance premium when claim amounts are heavy-tailed. We propose two methods to estimate the reinsurance premium. The first one is a non-parametric estimator based directly on the empirical distribution, and the second one is a semi-parametric estimator. Under some regularity conditions, asymptotic normalities of the two estimators are established, and an algorithm for calculating confidence bounds is presented. Further, finite sample behaviors of the two estimators are compared by simulation studies.
Funding Statement
No funding was received for this study.
Acknowledgments
The authors would like to thank the Editor and the referee for careful reading and useful comments which greatly improved the paper.
Citation
Qian Xiong. Zuoxiang Peng. Saralees Nadarajah. "Reinsurance premium estimation for heavy-tailed claim amounts." Braz. J. Probab. Stat. 38 (1) 32 - 52, March 2024. https://doi.org/10.1214/23-BJPS588
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