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On univariate extreme value statistics and the estimation of reinsurance premiums. (English) Zbl 1168.62392

Summary: We consider the estimation of insurance premiums for excess-of-loss reinsurance policies in excess of a high retention level. Special attention is paid to Wang’s premium principle and heavy-tailed distributions, for which estimators of small exceedance probabilities allow the estimation of reinsurance premiums. Next to the construction of estimators, we also consider the corresponding asymptotic results and illustrate the finite sample behavior through a real insurance application as well as simulations.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62G32 Statistics of extreme values; tail inference
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