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A new efficient method for estimating the Gerber–Shiu function in the classical risk model

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  • Zhimin Zhang
  • Wen Su

Abstract

In this paper, we propose a new efficient method for estimating the Gerber–Shiu discounted penalty function in the classical risk model. We develop the Gerber–Shiu function on the Laguerre basis, and then estimate the unknown coefficients based on sample information on claim numbers and individual claim sizes. The convergence rate of the estimate is derived. Some simulation examples are illustrated to show that the estimate performs very well when the sample size is finite. We also show that the proposed estimate outperforms other estimates in the simulation studies.

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  • Zhimin Zhang & Wen Su, 2018. "A new efficient method for estimating the Gerber–Shiu function in the classical risk model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(5), pages 426-449, May.
    • Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:426-449
    DOI: 10.1080/03461238.2017.1371068
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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. Su, Wen & Yong, Yaodi, 2024. "Estimating a VaR-type ruin measure by Laguerre series expansion in classical compound Poisson risk model," Statistics & Probability Letters, Elsevier, vol. 205(C).
    3. 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.
    4. Deelstra, Griselda & Hieber, Peter, 2023. "Randomization and the valuation of guaranteed minimum death benefits," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1218-1236.

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