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

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  • Yasutaka Shimizu

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.

Suggested Citation

  • Yasutaka Shimizu, 2012. "Non-parametric estimation of the Gerber–Shiu function for the Wiener–Poisson risk model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2012(1), pages 56-69.
    • Handle: RePEc:taf:sactxx:v:2012:y:2012:i:1:p:56-69
    DOI: 10.1080/03461238.2010.523515
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    Cited by:

    1. Zan Yu & Lianzeng Zhang, 2024. "Computing the Gerber-Shiu function with interest and a constant dividend barrier by physics-informed neural networks," Papers 2401.04378, arXiv.org.

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