References
- Asmussen, S. 2003. Applied probability and queues. 2nd ed. New York: Springer.
- Chen, Y., K. C. Yuen, and K. W. Ng. 2011. Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims. Applied Stochastic Models in Business and Industry 27 (3):290–300. doi:10.1002/asmb.834.
- 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.
- Chistyakov, V. P. 1964. A theorem on sums of independent positive random variables and its applications to branching process. Theory of Probability & Its Applications 9 (4):640–48. doi:10.1137/1109088.
- Embrechts, P., C. Klüppelberg, and T. Mikosch. 1997. Modelling extremal events for insurance and finance. Berlin: Springer.
- Foss, S., D. Korshunov, and S. Zachary. 2011. An introduction to heavy-tailed and subexponential distributions. New York: Springer.
- 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.
- Hao, X., and Q. Tang. 2008. A uniform asymptotic estimate for discounted aggregate claims with subexponential tails. Insurance: Mathematics and Economics 43 (1):116–20. doi:10.1016/j.insmatheco.2008.03.009.
- Lehmann, E. 1966. Some concepts of dependence. The Annals of Mathematical Statistics 37 (5):1137–53. doi:10.1214/aoms/1177699260.
- Li, J., Z. Liu, and Q. Tang. 2007. On the ruin probabilities of a bidimensional perturbed risk model. Insurance: Mathematics and Economics 41 (1):185–95. doi:10.1016/j.insmatheco.2006.10.012.
- Lu, D., and B. Zhang. 2016. Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims. Statistics & Probability Letters 114:20–29. doi:10.1016/j.spl.2016.03.005.
- Ko, B., and Q. Tang. 2008. Sums of dependent nonnegative random variables with subexponential tail. Journal of Applied Probability. 45:5–95.
- Stein, C. 1946. A note on cumulative sums. The Annals of Mathematical Statistics 17 (4):498–99. doi:10.1214/aoms/1177730890.
- Tang, Q., and G. Tsitsiashvili. 2003. Randomly weighted sums of subexponential random variables with application to ruin theory. Extremes 6 (3):171–88. doi:10.1023/B:EXTR.0000031178.19509.57.
- 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.
- Zhang, Y., and W. Wang. 2012. Ruin probabilities of a bidimensional risk model with investment. Statistics & Probability Letters 82 (1):130–38. doi:10.1016/j.spl.2011.09.010.