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A revisit to ruin probabilities in the presence of heavy-tailed insurance and financial risks

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  • Chen, Yiqing
  • Yuan, Zhongyi

Abstract

Recently, Sun and Wei (2014) studied the finite-time ruin probability under a discrete-time insurance risk model, in which the one-period insurance and financial risks are assumed to be independent and identically distributed copies of a random pair (X,Y). For the heavy-tailed case, under a restriction on the dependence structure of (X,Y), they established an asymptotic formula for the finite-time ruin probability. In this paper we make an effort to remove this restriction as it excludes the cases with asymptotically dependent X and Y. We also extend the study to the infinite-time ruin probability. Employing a multivariate regular variation framework, we simplify the formula so that it shows in a transparent way how the ruin probabilities are affected by the tail dependence of (X,Y).

Suggested Citation

  • Chen, Yiqing & Yuan, Zhongyi, 2017. "A revisit to ruin probabilities in the presence of heavy-tailed insurance and financial risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 75-81.
    • Handle: RePEc:eee:insuma:v:73:y:2017:i:c:p:75-81
    DOI: 10.1016/j.insmatheco.2017.01.005
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    References listed on IDEAS

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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
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    3. Norberg, Ragnar, 1999. "Ruin problems with assets and liabilities of diffusion type," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 255-269, June.
    4. Klüppelberg, Claudia & Kostadinova, Radostina, 2008. "Integrated insurance risk models with exponential Lévy investment," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 560-577, April.
    5. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
    6. Chen, Yiqing & Ng, Kai W., 2007. "The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 415-423, May.
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    8. Henrik Hult & Filip Lindskog, 2011. "Ruin probabilities under general investments and heavy-tailed claims," Finance and Stochastics, Springer, vol. 15(2), pages 243-265, June.
    9. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
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    Cited by:

    1. Yang Yang & Shuang Liu & Kam Chuen Yuen, 2022. "Second-Order Tail Behavior for Stochastic Discounted Value of Aggregate Net Losses in a Discrete-Time Risk Model," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2600-2621, December.
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    3. 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.

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