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Phase-type Approximation of the Gerber-Shiu Function

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  • Kazutoshi Yamazaki

Abstract

The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation requires the evaluation of the overshoot/undershoot distributions of the surplus process at ruin. In this paper, we use the recent developments of the fluctuation theory and approximate it in a closed form by fitting the underlying process by phase-type Levy processes. A sequence of numerical results are given.

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  • Kazutoshi Yamazaki, 2017. "Phase-type Approximation of the Gerber-Shiu Function," Papers 1701.02798, arXiv.org.
    • Handle: RePEc:arx:papers:1701.02798
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    Cited by:

    1. Emilio Gómez-Déniz & José María Sarabia & Enrique Calderín-Ojeda, 2019. "Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem," Risks, MDPI, vol. 7(2), pages 1-16, June.
    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.
    3. 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.
    4. Franck Adékambi & Kokou Essiomle, 2020. "Ruin Probability for Stochastic Flows of Financial Contract under Phase-Type Distribution," Risks, MDPI, vol. 8(2), pages 1-21, May.

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