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Estimating the Gerber–Shiu function by Fourier–Sinc series expansion

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  • Zhimin Zhang

Abstract

In this paper, we consider the nonparametric estimation of the Gerber–Shiu function in a compound Poisson risk model perturbed by diffusion. We present a more efficient estimator based on Fourier–Sinc series expansion. Our estimator is easily computed and has a faster convergence rate. Some simulation examples are provided to show that the estimator performs well when the sample size is finite.

Suggested Citation

  • Zhimin Zhang, 2017. "Estimating the Gerber–Shiu function by Fourier–Sinc series expansion," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(10), pages 898-919, November.
    • Handle: RePEc:taf:sactxx:v:2017:y:2017:i:10:p:898-919
    DOI: 10.1080/03461238.2016.1268541
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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.
    2. Kang Hu & Ya Huang & Yingchun Deng, 2023. "Estimating the Gerber–Shiu Function in the Two-Sided Jumps Risk Model by Laguerre Series Expansion," Mathematics, MDPI, vol. 11(9), pages 1-30, April.

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