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Distributional study of finite-time ruin related problems for the classical risk model

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  • Li, Shuanming
  • Lu, Yi

Abstract

In this paper, we study some finite-time ruin related problems for the classical risk model. We demonstrate that some techniques recently developed in [37] and [6] can be used to study the joint distribution of the time of ruin and the maximum surplus prior to ruin, the joint distribution of the time of ruin and the maximum severity of ruin, and the distribution of the two-sided first exit time. Especially, by solving a Seal’s type partial integro-differential equation we obtain an explicit (integral) expression for the finite-time Gerber–Shiu function, which is expressed in terms of the (infinite time) Gerber–Shiu function introduced in [12].

Suggested Citation

  • Li, Shuanming & Lu, Yi, 2017. "Distributional study of finite-time ruin related problems for the classical risk model," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 319-330.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:319-330
    DOI: 10.1016/j.amc.2017.07.054
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    1. Shuanming Li & Yi Lu & Can Jin, 2016. "Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 747-764, September.
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    1. Landriault, David & Li, Bin & Shi, Tianxiang & Xu, Di, 2019. "On the distribution of classic and some exotic ruin times," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 38-45.
    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. Bihao Su & Chenglong Xu & Jingchao Li, 2022. "A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation," Mathematics, MDPI, vol. 10(9), pages 1-21, May.

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