Non-parametric estimation of the Gerber-Shiu function for the Wiener-Poisson risk model

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Abstract

A non-parametric estimator of the Gerber-Shiu function is proposed for a risk process with a compound Poisson claim process plus a diffusion perturbation; the Wiener-Poisson risk model. The estimator is based on a regularized inversion of an empirical-type estimator of the Laplace transform of the Gerber-Shiu function. We show the weak consistency of the estimator in the sense of an integrated squared error with the rate of convergence.

Original languageEnglish
Pages (from-to)56-69
Number of pages14
JournalScandinavian Actuarial Journal
Issue number1
DOIs
Publication statusPublished - 2012 Mar
Externally publishedYes

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Keywords

  • Empirical estimator
  • Laplace transform
  • Regularized inversion
  • Risk model perturbed by diffusions
  • The expected discounted penalty function

ASJC Scopus subject areas

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

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