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Asymptotics for the ruin probabilities of a two‐dimensional renewal risk model with heavy‐tailed claims

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  • Yiqing Chen
  • Kam C. Yuen
  • Kai W. Ng

Abstract

In this paper, we consider two dependent classes of insurance business with heavy‐tailed claims. The dependence comes from the assumption that claim arrivals of the two classes are governed by a common renewal counting process. We study two types of ruin in the two‐dimensional framework. For each type of ruin, we establish an asymptotic formula for the finite‐time ruin probability. These formulae possess a certain uniformity feature in the time horizon. Copyright © 2010 John Wiley & Sons, Ltd.

Suggested Citation

  • Yiqing Chen & Kam C. Yuen & Kai W. Ng, 2011. "Asymptotics for the ruin probabilities of a two‐dimensional renewal risk model with heavy‐tailed claims," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 27(3), pages 290-300, May.
    • Handle: RePEc:wly:apsmbi:v:27:y:2011:i:3:p:290-300
    DOI: 10.1002/asmb.834
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    Cited by:

    1. Li, Jinzhu, 2022. "Asymptotic analysis of a dynamic systemic risk measure in a renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 38-56.
    2. Gordienko, E. & Vázquez-Ortega, P., 2018. "Continuity inequalities for multidimensional renewal risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 48-54.
    3. Albrecher, Hansjörg & Cheung, Eric C.K. & Liu, Haibo & Woo, Jae-Kyung, 2022. "A bivariate Laguerre expansions approach for joint ruin probabilities in a two-dimensional insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 96-118.
    4. Shijie Wang & Yueli Yang & Yang Liu & Lianqiang Yang, 2023. "Asymptotics for a Bidimensional Renewal Risk Model with Subexponential Main Claims and Delayed Claims," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-13, September.

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