Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus

Yasutaka Shimizu, Zhimin Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


Consider an insurance surplus process driven by a Lévy subordinator, which is observed at discrete time points. An estimator of the Gerber–Shiu function is proposed via the empirical Fourier transform of the Gerber–Shiu function. By evaluating its mean squared error, we show the L2-consistency of the estimator under the assumption of high-frequency observation of the surplus process in a long term. Simulation studies are also presented to show the finite sample performance of the proposed estimator.

Original languageEnglish
Pages (from-to)84-98
Number of pages15
JournalInsurance: Mathematics and Economics
Publication statusPublished - 2017 May 1


  • Estimation
  • Fourier inversion
  • Gerber–Shiu function
  • L-consistency
  • Lévy risk model

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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