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Estimating the Gerber-Shiu function under a risk model with stochastic income by Laguerre series expansion

Author

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  • Wen Su
  • Benxuan Shi
  • Yunyun Wang

Abstract

In this paper, we concern the statistical estimation of the Gerber-Shiu function under a risk model with stochastic premiums. We express the Gerber-Shiu function by Laguerre series expansion and estimate it based on observed information. Moreover, we study the convergence rate of our proposed estimator and illustrate the excellent performance of the estimator by simulations with finite sample size.

Suggested Citation

  • Wen Su & Benxuan Shi & Yunyun Wang, 2020. "Estimating the Gerber-Shiu function under a risk model with stochastic income by Laguerre series expansion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(23), pages 5686-5708, December.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:23:p:5686-5708
    DOI: 10.1080/03610926.2019.1620782
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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. 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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