Estimation of the expected discounted penalty function for Lévy insurance risks

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

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
Volume20
Issue number2
DOIs
Publication statusPublished - 2011 Jun
Externally publishedYes

Fingerprint

Penalty Function
Insurance
Estimator
Subordinator
Risk Process
Laplace
Laplace transform
Inversion
Asymptotic Behavior
Estimate
Insurance risk
Expected discounted penalty function
Framework
Asymptotic behavior
Risk process

Keywords

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

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Estimation of the expected discounted penalty function for Lévy insurance risks. / Shimizu, Yasutaka.

In: Mathematical Methods of Statistics, Vol. 20, No. 2, 06.2011, p. 125-149.

Research output: Contribution to journalArticle

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