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Estimating the time value of ruin in a Lévy risk model under low-frequency observation

Author

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  • Wang, Wenyuan
  • Xie, Jiayi
  • Zhang, Zhimin

Abstract

In this paper, we consider statistical estimation of the time value of ruin in a Lévy risk model. Suppose that the aggregate claims process of an insurance company is modeled by a pure jump Lévy subordinator, and we can observe the data set on the aggregate claims based on low-frequency sampling. The time value of ruin is estimated by the Fourier-cosine method, and the uniform convergence rate is also derived. Through a lot of simulation studies, we show that our estimators are very effective when the sample size is finite.

Suggested Citation

  • Wang, Wenyuan & Xie, Jiayi & Zhang, Zhimin, 2022. "Estimating the time value of ruin in a Lévy risk model under low-frequency observation," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 133-157.
    • Handle: RePEc:eee:insuma:v:104:y:2022:i:c:p:133-157
    DOI: 10.1016/j.insmatheco.2022.02.006
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    Cited by:

    1. 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.
    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.
    3. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.

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