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Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion

Author

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  • Wen Su

    (School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China)

  • Yunyun Wang

    (Department of Econometrics and Business Statistics, School of Business, Monash University, Melbourne 3800, Australia)

Abstract

In this paper, we propose an estimator for the Gerber–Shiu function in a pure-jump Lévy risk model when the surplus process is observed at a high frequency. The estimator is constructed based on the Fourier–Cosine series expansion and its consistency property is thoroughly studied. Simulation examples reveal that our estimator performs better than the Fourier transform method estimator when the sample size is finite.

Suggested Citation

  • Wen Su & Yunyun Wang, 2021. "Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1402-:d:576424
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    References listed on IDEAS

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    Cited by:

    1. 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.
    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.

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