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Estimating the Gerber-Shiu Function in a Compound Poisson Risk Model with Stochastic Premium Income

Author

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  • Yunyun Wang
  • Wenguang Yu
  • Yujuan Huang

Abstract

In this paper, we consider the compound Poisson risk model with stochastic premium income. We propose a new estimation of Gerber-Shiu function by an efficient method: Fourier-cosine series expansion. We show that the estimator is easily computed and has a fast convergence rate. Some simulation examples are illustrated to show that the estimation has a good performance when the sample size is finite.

Suggested Citation

  • Yunyun Wang & Wenguang Yu & Yujuan Huang, 2019. "Estimating the Gerber-Shiu Function in a Compound Poisson Risk Model with Stochastic Premium Income," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-18, July.
    • Handle: RePEc:hin:jnddns:5071268
    DOI: 10.1155/2019/5071268
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    Cited by:

    1. 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.
    2. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    3. Wenguang Yu & Yaodi Yong & Guofeng Guan & Yujuan Huang & Wen Su & Chaoran Cui, 2019. "Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    4. Olena Ragulina & Jonas Šiaulys, 2020. "Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy," Mathematics, MDPI, vol. 8(11), pages 1-35, October.

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