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Ruin probabilities of a two-dimensional risk model with dependent risks of heavy tail

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  • Shen, Xinmei
  • Zhang, Yi

Abstract

This paper considers a two-dimensional discrete time risk model with constant interest rates, and individual net losses in ERV(−α,−β), the class of extended regular variations with indices 0<α≤β<∞. Some asymptotic results for both finite-time and infinite-time ruin probabilities under two types of ruin times are established. The two components of net losses are allowed to be generally dependent.

Suggested Citation

  • Shen, Xinmei & Zhang, Yi, 2013. "Ruin probabilities of a two-dimensional risk model with dependent risks of heavy tail," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1787-1799.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:7:p:1787-1799
    DOI: 10.1016/j.spl.2013.03.029
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    References listed on IDEAS

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    1. Cai, Jun & Li, Haijun, 2007. "Dependence properties and bounds for ruin probabilities in multivariate compound risk models," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 757-773, April.
    2. Zhang, Yi & Shen, Xinmei & Weng, Chengguo, 2009. "Approximation of the tail probability of randomly weighted sums and applications," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 655-675, February.
    3. Chan, Wai-Sum & Yang, Hailiang & Zhang, Lianzeng, 2003. "Some results on ruin probabilities in a two-dimensional risk model," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 345-358, July.
    4. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    5. 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.
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    Cited by:

    1. Xinmei Shen & Kailin Du, 2023. "Uniform Approximation for the Tail Behavior of Bidimensional Randomly Weighted Sums," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-25, March.
    2. Fu, Ke-Ang & Ng, Cheuk Yin Andrew, 2017. "Uniform asymptotics for the ruin probabilities of a two-dimensional renewal risk model with dependent claims and risky investments," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 227-235.

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