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On the Gerber–Shiu function with random discount rate

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  • Houchun Wang
  • Nengxiang Ling

Abstract

In this paper, we study the Gerber–Shiu (G-S) function for the classical risk model, in which the discount rate is generalized from a constant to a random variable. The discounted interest force accumulated process is modeled by a Poisson process and a Gaussian process for the G-S function. In terms of the standard techniques in ruin theory, we derive the integro-differential equation and the defective renewal equation satisfied by the G-S function. Then, the asymptotic formula for the G-S function is obtained using the renewal theory.

Suggested Citation

  • Houchun Wang & Nengxiang Ling, 2017. "On the Gerber–Shiu function with random discount rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 210-220, January.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:1:p:210-220
    DOI: 10.1080/03610926.2014.988265
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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. 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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