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Nonparametric statistical analysis of an upper bound of the ruin probability under large claims. (English) Zbl 1226.91023

Summary: The classical Poisson risk model is considered. The claims are supposed to be modeled by heavy-tailed distributions, so that the moment generating function does not exist. The attention is focused on the probability of ruin. We first provide a nonparametric estimator of an upper bound of the ruin probability by Willmot and Lin. Then, its asymptotic behavior is studied. Asymptotic confidence intervals are studied, as well as bootstrap confidence intervals. Results for possibly unstable models are also obtained.

MSC:

91B30 Risk theory, insurance (MSC2010)
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62G32 Statistics of extreme values; tail inference
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