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Asymptotic infinite-time ruin probabilities for a bidimensional time-dependence risk model with heavy-tailed claims

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Abstract

The paper studies asymptotic infinite-time ruin probabilities for a bidimensional time-dependent risk model, in which two insurance companies divide between them both the premium income and the aggregate claims in different positive proportions (modeling an insurer–reinsurer scenario, where the reinsurer takes over a proportion of the insurer’s losses). In the model, the claim sizes and the inter-arrival times correspondingly form a sequence of independent and identically distributed random vectors, where each pair of the vectors follows the time-dependence structure. Under the assumption that the claim sizes have consistently varying tails, asymptotic formulas for two kinds of infinite-time ruin probabilities are derived.

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Acknowledgements

The authors would fully appreciate the referees and editors making their insightful and helpful suggestions, which help to improve the presentation of this paper greatly. This paper was supported by National Natural Science Foundation of China (No. 11401415).

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Authors and Affiliations

  1. School of Mathematical Sciences, Soochow University, Suzhou, 215006, China

    Bingjie Wang, Jigao Yan & Dongya Cheng

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  1. Bingjie Wang
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  2. Jigao Yan
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  3. Dongya Cheng
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Correspondence to Dongya Cheng.

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Wang, B., Yan, J. & Cheng, D. Asymptotic infinite-time ruin probabilities for a bidimensional time-dependence risk model with heavy-tailed claims. Japan J. Indust. Appl. Math. 39, 177–194 (2022). https://doi.org/10.1007/s13160-021-00487-7

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  • DOI: https://doi.org/10.1007/s13160-021-00487-7

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