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The Gerber-Shiu discounted penalty function for classical risk model with a two-step premium rate

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  • Zhang, H.Y.
  • Zhou, M.
  • Guo, J.Y.

Abstract

The paper studies the expected value of a discounted penalty function for a classical risk model with a two-step premium rate. In this model, we firstly derive and solve an integro-differential equation for the Gerber-Shiu discounted penalty function, then use this result to obtain the expressions of ruin probability and the joint distribution of the surplus immediately before ruin and the deficit at ruin.

Suggested Citation

  • Zhang, H.Y. & Zhou, M. & Guo, J.Y., 2006. "The Gerber-Shiu discounted penalty function for classical risk model with a two-step premium rate," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1211-1218, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1211-1218
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    References listed on IDEAS

    as
    1. Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 63-84, September.
    2. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    3. Zhou, Xiaowen, 2004. "When does surplus reach a certain level before ruin?," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 553-561, December.
    4. Gerber, Hans U. & Shiu, Elias S. W., 1997. "The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 129-137, November.
    5. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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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. Bratiychuk, M.S. & Derfla, D., 2007. "On a modification of the classical risk process," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 156-162, July.
    3. Boxma, Onno & Frostig, Esther & Perry, David & Yosef, Rami, 2017. "A state dependent reinsurance model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 170-181.
    4. 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.
    5. Jiechang Ruan & Wenguang Yu & Ke Song & Yihan Sun & Yujuan Huang & Xinliang Yu, 2019. "A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model," Mathematics, MDPI, vol. 7(10), pages 1-12, September.

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