Parametric inference for ruin probability in the classical risk model

Takayoshi Oshime, Yasutaka Shimizu

Research output: Contribution to journalArticlepeer-review

Abstract

Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability.

Original languageEnglish
Pages (from-to)28-37
Number of pages10
JournalStatistics and Probability Letters
Volume133
DOIs
Publication statusPublished - 2018 Feb

Keywords

  • Asymptotic confidence interval
  • Cramér approximation
  • Delta method
  • Ruin probability
  • Small claims

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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