Estimation of the expected discounted penalty function for Lévy insurance risks

Y. Shimizu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


We consider a generalized risk process which consists of a subordinator plus a spectrally negative Lévy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.

Original languageEnglish
Pages (from-to)125-149
Number of pages25
JournalMathematical Methods of Statistics
Issue number2
Publication statusPublished - 2011 Jun
Externally publishedYes


  • ISE-consistency
  • Lévy risk process
  • discrete observations
  • expected discounted penalty function
  • regularized Laplace inversion

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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