Asymptotic behavior for sum ruin probability of a generalized bidimensional risk model with heavy-tailed claims

References

• Cheng, D. 2021. Uniform asymptotics for the finite-time ruin probability of a generalized bidimensional risk model with Brownian perturbations. Stochastics 93 (1):56–71. doi:10.1080/17442508.2019.1708362.
   Web of Science ®Google Scholar
• Cheng, D., and C. Yu. 2019. Uniform asymptotics for the ruin probabilities in a bidimensional renewal risk model with strongly subexponential claims. Stochastics 91 (5):643–56. doi:10.1080/17442508.2018.1539088.
   Web of Science ®Google Scholar
• Cheng, D., Y. Yang, and X. Wang. 2020. Asymptotic finite-time ruin probabilities in a dependent bidimensional renewal risk model with subexponential claims. Japan Journal of Industrial and Applied Mathematics 37 (3):657–75. doi:10.1007/s13160-020-00418-y.
   Web of Science ®Google Scholar
• Cheng, F., D. Cheng, and Z. Chen. 2021. Asymptotic behavior for finite-time ruin probabilities in a generalized bidimensional risk model with subexponential claims. Japan Journal of Industrial and Applied Mathematics 38 (3):947–63. doi:10.1007/s13160-021-00472-0.
   Web of Science ®Google Scholar
• Cline, D. B., and G. Samorodnitsky. 1994. Subexponentiality of the product of independent random variables. Stochastic Processes and Their Applications 49 (1):75–98. doi:10.1016/0304-4149(94)90113-9.
   Web of Science ®Google Scholar
• Embrechts, P., and C. M. Goldie. 1980. On closure and factorization properties of subexponential and related distributions. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 29 (2):243–56. doi:10.1017/S1446788700021224.
   Google Scholar
• Embrechts, P., C. Klüppelberg, and T. Mikosch. 1997. Modelling extremal events for insurance and finance. Berlin: Springer-Verlag.
   Google Scholar
• Foss, S., D. Korshunov, and S. Zachary. 2011. An introduction to heavy-tailed and subexponential distributions. New York: Springer.
   Google Scholar
• Fu, K. A., C. Ni, and H. Chen. 2020. A Particular bidimensional time-dependent renewal risk model with constant interest rates. Probability in the Engineering and Informational Sciences 34 (2):172–82. doi:10.1017/S0269964819000020.
   Web of Science ®Google Scholar
• Gao, Q., and X. Yang. 2014. Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest. Journal of Mathematical Analysis and Applications 419 (2):1193–213. doi:10.1016/j.jmaa.2014.05.069.
   Web of Science ®Google Scholar
• Geng, B., R. Ji, and S. Wang. 2019. Tail probability of randomly weighted sums of dependent subexponential random variables with applications to risk theory. Journal of Mathematical Analysis and Applications 480 (1):123389. doi:10.1016/j.jmaa.2019.123389.
   Web of Science ®Google Scholar
• Gong, Y., Y. Yang, and J. Liu. 2021. On the Kesten-type inequality for randomly weighted sums with applications to an operational risk model. Filomat 35 (6):1879–88. doi:10.2298/FIL2106879G.
   Web of Science ®Google Scholar
• Ko, B., and Q. Tang. 2008. Sums of dependent nonnegative random variables with subexponential tails. Journal of Applied Probability 45 (1):85–94. doi:10.1239/jap/1208358953.
   Web of Science ®Google Scholar
• Li, J. 2017. A note on the finite-time ruin probability of a renewal risk model with Brownian perturbation. Statistics and Probability Letters 127:49–55. doi:10.1016/j.spl.2017.03.028.
   Web of Science ®Google Scholar
• Piterbarg, V. I. 1996. Asymptotic methods in the theory of gaussian processes and fields, Vol. 148. American Mathematical Society, Providence.
   Google Scholar
• Stein, C. 1946. A note on cumulative sums. The Annals of Mathematical Statistics 17 (4):498–9. doi:10.1214/aoms/1177730890.
   Google Scholar
• Sun, H., B. Geng, and S. Wang. 2020. Asymptotic sum-ruin probability for a bidimensional risk model with common shock dependence. Stochastics 91 (5):643–56.
   Google Scholar
• Tang, Q., and G. Tsitsiashvili. 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 108 (2):299–325. doi:10.1016/j.spa.2003.07.001.
   Web of Science ®Google Scholar
• Wang, S., H. Qian, H. Sun, and B. Geng. 2021. Uniform asymptotics for ruin probabilities of a non standard bidimensional perturbed risk model with subexponential claims. Communications in Statistics-Theory and Methods:1–16. doi:10.1080/03610926.2021.1882496 (to appear).
   Web of Science ®Google Scholar
• Yang, K., J. Wang, Z. Liu, and Zhang, Y. 2019. Asymptotics for a bidimensional risk model with two geometric Lévy price processes. Journal of Industrial & Management Optimization 15 (2):481–505. doi:10.3934/jimo.2018053.
   Web of Science ®Google Scholar
• Yang, Y., J. Lin, C. Huang, and X. Ma. 2012. The finite-time ruin probability in two non-standard renewal risk models with constant interest rate and dependent subexponential claims. Journal of the Korean Statistical Society 41 (2):213–24. doi:10.1016/j.jkss.2011.08.006.
   Web of Science ®Google Scholar
• Zhang, Y., and F. Cheng. 2017. Asymptotic tail behavior of a random sum with conditionally dependent subexponential summands. Communications in Statistics-Theory and Methods 46 (12):5888–95. doi:10.1080/03610926.2015.1112916.
   Web of Science ®Google Scholar