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Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return

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  • Li, Jinzhu

Abstract

This paper is devoted to asymptotic analysis for a multi-dimensional risk model with a general dependence structure and stochastic return driven by a geometric Lévy process. We take into account both the dependence among the claim sizes from different lines of businesses and that between the claim sizes and their common claim-number process. Under certain mild technical conditions, we obtain for two types of ruin probabilities precise asymptotic expansions which hold uniformly for the whole time horizon.

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  • Li, Jinzhu, 2016. "Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 195-204.
    • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:195-204
    DOI: 10.1016/j.insmatheco.2016.09.003
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    12. Xiaohu Li & Jintang Wu & Jinsen Zhuang, 2015. "Asymptotic Multivariate Finite-time Ruin Probability with Statistically Dependent Heavy-tailed Claims," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 463-477, June.
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    14. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.
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    16. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
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    2. Li, Jinzhu, 2022. "Asymptotic results on marginal expected shortfalls for dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 146-168.
    3. Guo, Fenglong, 2022. "Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factors," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    4. Dawei Lu & Ting Li & Meng Yuan & Xinmei Shen, 2024. "Asymptotic Finite-Time Ruin Probabilities for a Multidimensional Risk Model with Subexponential Claims," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-28, September.
    5. Yuan, Meng & Lu, Dawei, 2023. "Asymptotics for a time-dependent by-claim model with dependent subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 120-141.
    6. Ming Cheng & Dingcheng Wang, 2023. "Uniform Asymptotic Estimate for the Ruin Probability in a Renewal Risk Model with Cox–Ingersoll–Ross Returns," Mathematics, MDPI, vol. 11(5), pages 1-10, March.

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