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Nonparametric statistical analysis of an upper bound of the ruin probability under large claims

Abstract

In this paper, 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.

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Correspondence to Pier Luigi Conti.

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Conti, P.L., Masiello, E. Nonparametric statistical analysis of an upper bound of the ruin probability under large claims. Extremes 13, 439–461 (2010). https://doi.org/10.1007/s10687-009-0094-6

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  • DOI: https://doi.org/10.1007/s10687-009-0094-6

Keywords

  • Poisson risk model
  • Probability of ruin
  • Nonparametric estimation
  • Asymptotics
  • Heavy-tailed distribution

AMS 2000 Subject Classifications

  • 62G08
  • 62G20
  • 62G32