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Asymptotic ruin probabilities for a multidimensional renewal risk model with multivariate regularly varying claims

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  • Konstantinides, Dimitrios G.
  • Li, Jinzhu

Abstract

This paper studies a continuous-time multidimensional risk model with constant force of interest and dependence structures among random factors involved. The model allows a general dependence among the claim-number processes from different insurance businesses. Moreover, we utilize the framework of multivariate regular variation to describe the dependence and heavy-tailed nature of the claim sizes. Some precise asymptotic expansions are derived for both finite-time and infinite-time ruin probabilities.

Suggested Citation

  • Konstantinides, Dimitrios G. & Li, Jinzhu, 2016. "Asymptotic ruin probabilities for a multidimensional renewal risk model with multivariate regularly varying claims," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 38-44.
    • Handle: RePEc:eee:insuma:v:69:y:2016:i:c:p:38-44
    DOI: 10.1016/j.insmatheco.2016.04.003
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    References listed on IDEAS

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    1. Qihe Tang & Zhongyi Yuan, 2013. "Asymptotic Analysis of the Loss Given Default in the Presence of Multivariate Regular Variation," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(3), pages 253-271.
    2. Li, Junhai & Liu, Zaiming & Tang, Qihe, 2007. "On the ruin probabilities of a bidimensional perturbed risk model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 185-195, July.
    3. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    4. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    5. 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.
    6. Zhang, Yuanyuan & Wang, Wensheng, 2012. "Ruin probabilities of a bidimensional risk model with investment," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 130-138.
    7. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
    8. Yang, Haizhong & Li, Jinzhu, 2014. "Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 185-192.
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    Cited by:

    1. Cheng, Ming & Konstantinides, Dimitrios G. & Wang, Dingcheng, 2022. "Uniform asymptotic estimates in a time-dependent risk model with general investment returns and multivariate regularly varying claims," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    2. Anita Behme & Philipp Lukas Strietzel, 2021. "A $$2~{\times }~2$$ 2 × 2 random switching model and its dual risk model," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 27-64, October.
    3. 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.
    4. Andreas Karathanasopoulos & Chia Chun Lo & Xiaorong Ma & Zhenjiang Qin, 2021. "Maintaining cost and ruin probability," Review of Quantitative Finance and Accounting, Springer, vol. 57(2), pages 759-793, August.
    5. Yiqing Chen & Jiajun Liu & Yang Yang, 2023. "Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    6. 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.

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