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

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21 Citations (Scopus)

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

Fingerprint

Gerber-Shiu Function
Nonparametric Estimation
Siméon Denis Poisson
Estimator
Integrated Squared Error
Weak Consistency
Compound Poisson
Risk Process
Nonparametric Estimator
Laplace transform
Inversion
Rate of Convergence
Model
Perturbation
Gerber-Shiu function
Nonparametric estimation
Risk model

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

Cite this

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KW - The expected discounted penalty function

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