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

Yasutaka Shimizu

doi:10.1080/03461238.2010.523515

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

Yasutaka Shimizu^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

32 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 language	English
Pages (from-to)	56-69
Number of pages	14
Journal	Scandinavian Actuarial Journal
Issue number	1
DOIs	https://doi.org/10.1080/03461238.2010.523515
Publication status	Published - 2012 Mar
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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10.1080/03461238.2010.523515

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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.",

keywords = "Empirical estimator, Laplace transform, Regularized inversion, Risk model perturbed by diffusions, The expected discounted penalty function",

author = "Yasutaka Shimizu",

note = "Funding Information: The author expresses his sincere thanks to an anonymous referee for his/her accurate comments and instructions with the careful reading, which substantially improved the paper. This research was partially supported by the Ministry of Education, Science, Sports, and Culture; Grant-in-Aid for Young Scientists (B), 2009·2010, No. 21740073; and Japan Science and Technology Agency, CREST.",

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N1 - Funding Information: The author expresses his sincere thanks to an anonymous referee for his/her accurate comments and instructions with the careful reading, which substantially improved the paper. This research was partially supported by the Ministry of Education, Science, Sports, and Culture; Grant-in-Aid for Young Scientists (B), 2009·2010, No. 21740073; and Japan Science and Technology Agency, CREST.

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KW - Regularized inversion

KW - Risk model perturbed by diffusions

KW - The expected discounted penalty function

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

Abstract

Keywords

ASJC Scopus subject areas

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