참고문헌
- A. V. Asimit and A. L. Badescu, Extremes on the discounted aggregate claims in a time dependent risk model, Scand. Actuar. J. 2010 (2010), no. 2, 93-104. https://doi.org/10.1080/03461230802700897
- J. Cai and Q. Tang, On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications, J. Appl. Probab. 41 (2004), no. 1, 117-130. https://doi.org/10.1017/S002190020001408X
- Y. Chen, K. W. Ng, and K. C. Yuen, The maximum of randomly weighted sums with long tails in insurance and finance, Stoch. Anal. Appl. 29 (2011), no. 6, 1033-1044. https://doi.org/10.1080/07362994.2011.610163
- Y. Chen and K. C. Yuen, Sums of pairwise quasi-asymptotically independent random variables with consistent variation, Stoch. Models 25 (2009), no. 1, 76-89. https://doi.org/10.1080/15326340802641006
- P. Embrechts and C. M. Goldie, On closure and factorization properties of subexponential and related distributions, J. Austral. Math. Soc. Ser. A 29 (1980), no. 2, 243-256. https://doi.org/10.1017/S1446788700021224
- S. Foss, D. Korshunov, and S. Zachary, Convolutions of long-tailed and subexponential distributions, J. Appl. Probab. 46 (2009), no. 3, 756-767. https://doi.org/10.1017/S0021900200005866
- Q. Gao and Y. Wang, Randomly weighted sums with dominated varying-tailed increments and application to risk theory, J. Korean Statist. Soc. 39 (2010), no. 3, 305-314. https://doi.org/10.1016/j.jkss.2010.02.004
- J. Geluk and K. W. Ng, Tail behavior of negatively associated heavy-tailed sums, J. Appl. Probab. 43 (2006), no. 2, 587-593. https://doi.org/10.1017/S0021900200001844
- J. Geluk and Q. Tang, Asymptotic tail probabilities of sums of dependent subexponential random variables, J. Theoret. Probab. 22 (2009), no. 4, 871-882. https://doi.org/10.1007/s10959-008-0159-5
- T. Jiang, Y. Wang, Y. Chen, and H. Xu, Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model, Insurance Math. Econom. 64 (2015), 45-53. https://doi.org/10.1016/j.insmatheco.2015.04.006
- F. Kong and G. Zong, The finite-time ruin probability for ND claims with constant interest force, Statist. Probab. Lett. 78 (2008), no. 17, 3103-3109. https://doi.org/10.1016/j.spl.2008.05.036
- J. R. Leslie, On the non-closure under convolution of the subexponential family, J. Appl. Probab. 26 (1989), no. 1, 58-66. https://doi.org/10.1017/S0021900200041796
- J. Li, On pairwise quasi-asymptotically independent random variables and their applications, Statist. Probab. Lett. 83 (2013), no. 9, 2081-2087. https://doi.org/10.1016/j.spl.2013.05.023
- J. Li, Q. Tang, and R. Wu, Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model, Adv. in Appl. Probab. 42 (2010), no. 4, 1126-1146. https://doi.org/10.1017/S0001867800004559
- J. Li and R. Wu, Asymptotic ruin probabilities of the renewal model with constant interest force and dependent heavy-tailed claims, Acta Math. Appl. Sin. Engl. Ser. 27 (2011), no. 2, 329-338. https://doi.org/10.1007/s10255-011-0064-z
- X. Liu, Q. Gao, and Y. Wang, A note on a dependent risk model with constant interest rate, Statist. Probab. Lett. 82 (2012), no. 4, 707-712. https://doi.org/10.1016/j.spl.2011.12.016
- K. W. Ng, Q. Tang, and H. Yang, Maxima of sums of heavy-tailed random variables, Astin Bull. 32 (2002), no. 1, 43-55. https://doi.org/10.2143/AST.32.1.1013
- Q. Tang and G. Tsitsiashvili, Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks, Stochastic Process. Appl. 108 (2003), no. 2, 299-325. https://doi.org/10.1016/j.spa.2003.07.001
- Q. Tang and G. Tsitsiashvili, Randomly weighted sums of subexponential random variables with application to ruin theory, Extremes 6 (2003), no. 3, 171-188. https://doi.org/10.1023/B:EXTR.0000031178.19509.57
- Q. Tang and Z. Yuan, Randomly weighted sums of subexponential random variables with application to capital allocation, Extremes 17 (2014), no. 3, 467-493. https://doi.org/10.1007/s10687-014-0191-z
- K. Wang, Randomly weighted sums of dependent subexponential random variables, Lith. Math. J. 51 (2011), no. 4, 573-586. https://doi.org/10.1007/s10986-011-9149-x
- K. Wang, Y. Wang, and Q. Gao, Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate, Methodol. Comput. Appl. Probab. 15 (2013), no. 1, 109-124. https://doi.org/10.1007/s11009-011-9226-y
- T. Watanabe and K. Yamamuro, Ratio of the tail of an infinitely divisible distribution on the line to that of its Levy measure, Electron. J. Probab. 15 (2010), no. 2, 44-74.
- H. Xu, S. Foss, and Y. Wang, Convolution and convolution-root properties of long-tailed distributions, Extremes 18 (2015), no. 4, 605-628. https://doi.org/10.1007/s10687-015-0224-2
- Y. Yang, R. Leipus, and J. Siaulys, Tail probability of randomly weighted sums of subexponential random variables under a dependence structure, Statist. Probab. Lett. 82 (2012), no. 9, 1727-1736. https://doi.org/10.1016/j.spl.2012.05.016
- Y. Yang, R. Leipus, and J. Siaulys, Closure property and maximum of randomly weighted sums with heavy tailed increments, Statist. Probab. Lett. 91 (2014), 162-170. https://doi.org/10.1016/j.spl.2014.04.020
- C. Zhang, Uniform asymptotics for the tail probability of weighted sums with heavy tails, Statist. Probab. Lett. 94 (2014), 221-229. https://doi.org/10.1016/j.spl.2014.07.022
- C. Zhu and Q. Gao, The uniform approximation of the tail probability of the randomly weighted sums of subexponential random variables, Statist. Probab. Lett. 78 (2008), no. 15, 2552-2558. https://doi.org/10.1016/j.spl.2008.02.036