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Asymptotics for random-time ruin probability in a time-dependent renewal risk model with subexponential claims
1. | International Center of Management Science and Engineering, School of Management and Engineering, Nanjing University, Nanjing, 210093, China, China, China |
2. | Department of Mathematics, Zaozhuang University, Zaozhuang, 277160, China |
References:
[1] |
A. Asimit and A. Badescu, Extremes on the discounted aggregate claims in a time dependent risk model, Scand. Actuar. J., (2010), 93-104.
doi: 10.1080/03461230802700897. |
[2] |
N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
doi: 10.1017/CBO9780511721434. |
[3] |
Y. Chen and K. Yuen, Sums of pairwise quasi-asymptotically independent random variables with consistent variation, Stochastic Models, 25 (2009), 76-89.
doi: 10.1080/15326340802641006. |
[4] |
D. B. H. Cline and G. Samorodnitsky, Subexponentiality of the product of independent random variables, Stoch. Proc. Appl., 49 (1994), 75-98.
doi: 10.1016/0304-4149(94)90113-9. |
[5] |
P. Embrechts, C. Klüppelberg and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997.
doi: 10.1007/978-3-642-33483-2. |
[6] |
Q. Gao and D. Bao, Asymptotic ruin probabilities in a generalized jump-diffusion risk model with constant force of interest, J. Korean Math. Soc., 51 (2014), 735-749.
doi: 10.4134/JKMS.2014.51.4.735. |
[7] |
Q. Gao, N. Jin and H. Shen, Asymptotic behavior of the finite-time ruin probability with pairwise quasi-asymptotically independent claims and constant interest force, Rocky Mountain J. Math., 44 (2014), 1505-1528.
doi: 10.1216/RMJ-2014-44-5-1505. |
[8] |
Q. Gao and X. Liu, Uniform asymptotics for the finite-time ruin probability with upper tail asymptotically independent claims and constant force of interest, Stat. Probab. Lett., 83 (2013), 1527-1538.
doi: 10.1016/j.spl.2013.02.018. |
[9] |
Q. Gao and X. Yang, Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest, J. Math. Anal. Appl., 419 (2014), 1193-1213.
doi: 10.1016/j.jmaa.2014.05.069. |
[10] |
Q. Gao and Y. Yang, Uniform asymptotics for the finite-time ruin probability in a general risk model with pairwise quasi-asymptotically independent claims and constant interest force, Bull. Korean Math. Soc., 50 (2013), 611-626.
doi: 10.4134/BKMS.2013.50.2.611. |
[11] |
Q. Gao, E. Zhang and N. Jin, The ultimate ruin probability of a dependent delayed-claim risk model perturbed by diffusion with constant force of interest, to appear in Bull. Korean Math. Soc., (2014). |
[12] |
J. Kočetova, R. Leipus and J. Šiaulys, A property of the renewal counting process with application to the finite-time ruin probability, Lith. Math. J., 49 (2009), 55-61.
doi: 10.1007/s10986-009-9032-1. |
[13] |
R. Leipus and J. Šiaulys, Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes, Insurance Math. Econom., 40 (2007), 498-508.
doi: 10.1016/j.insmatheco.2006.07.006. |
[14] |
R. Leipus and J. Šiaulys, Asymptotic behaviour of the finite-time ruin probability in renewal risk model, Appl. Stoch. Models Bus. Ind., 25 (2009), 309-321.
doi: 10.1002/asmb.747. |
[15] |
J. Li, Q. Tang and R. Wu, Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model, Adv. Appl. Proba., 42 (2010), 1126-1146.
doi: 10.1239/aap/1293113154. |
[16] |
S. I. Resnick, Hidden regular variation, second order regular variation and asymptotic independence, Extrems, 5 (2002), 303-336.
doi: 10.1023/A:1025148622954. |
[17] |
Q. Tang, Asymptotics for the finite time ruin probability in the renewal model with consistent variation, Stoch. Models, 20 (2004), 281-297.
doi: 10.1081/STM-200025739. |
[18] |
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), 109-124.
doi: 10.1007/s11009-011-9226-y. |
[19] |
Y. Wang, Z. Cui, K. Wang and X. Ma, Uniform asymptotics of the finite-time ruin probability for all times, J. Math. Anal. Appl., 390 (2012), 208-223.
doi: 10.1016/j.jmaa.2012.01.025. |
[20] |
Y. Wang, Q. Gao, K. Wang and X. Liu, Random time ruin probability for the renewal risk model with heavy-tailed claims, J. Ind. Manag. Optim., 5 (2009), 719-736.
doi: 10.3934/jimo.2009.5.719. |
[21] |
Y. Yang, R. Leipus, J. Šiaulys and Y. Cang, Uniform estimates for the finite-time ruin probability in the dependent renewal risk model, J. Math. Anal. Appl., 383 (2011), 215-225.
doi: 10.1016/j.jmaa.2011.05.013. |
show all references
References:
[1] |
A. Asimit and A. Badescu, Extremes on the discounted aggregate claims in a time dependent risk model, Scand. Actuar. J., (2010), 93-104.
doi: 10.1080/03461230802700897. |
[2] |
N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
doi: 10.1017/CBO9780511721434. |
[3] |
Y. Chen and K. Yuen, Sums of pairwise quasi-asymptotically independent random variables with consistent variation, Stochastic Models, 25 (2009), 76-89.
doi: 10.1080/15326340802641006. |
[4] |
D. B. H. Cline and G. Samorodnitsky, Subexponentiality of the product of independent random variables, Stoch. Proc. Appl., 49 (1994), 75-98.
doi: 10.1016/0304-4149(94)90113-9. |
[5] |
P. Embrechts, C. Klüppelberg and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997.
doi: 10.1007/978-3-642-33483-2. |
[6] |
Q. Gao and D. Bao, Asymptotic ruin probabilities in a generalized jump-diffusion risk model with constant force of interest, J. Korean Math. Soc., 51 (2014), 735-749.
doi: 10.4134/JKMS.2014.51.4.735. |
[7] |
Q. Gao, N. Jin and H. Shen, Asymptotic behavior of the finite-time ruin probability with pairwise quasi-asymptotically independent claims and constant interest force, Rocky Mountain J. Math., 44 (2014), 1505-1528.
doi: 10.1216/RMJ-2014-44-5-1505. |
[8] |
Q. Gao and X. Liu, Uniform asymptotics for the finite-time ruin probability with upper tail asymptotically independent claims and constant force of interest, Stat. Probab. Lett., 83 (2013), 1527-1538.
doi: 10.1016/j.spl.2013.02.018. |
[9] |
Q. Gao and X. Yang, Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest, J. Math. Anal. Appl., 419 (2014), 1193-1213.
doi: 10.1016/j.jmaa.2014.05.069. |
[10] |
Q. Gao and Y. Yang, Uniform asymptotics for the finite-time ruin probability in a general risk model with pairwise quasi-asymptotically independent claims and constant interest force, Bull. Korean Math. Soc., 50 (2013), 611-626.
doi: 10.4134/BKMS.2013.50.2.611. |
[11] |
Q. Gao, E. Zhang and N. Jin, The ultimate ruin probability of a dependent delayed-claim risk model perturbed by diffusion with constant force of interest, to appear in Bull. Korean Math. Soc., (2014). |
[12] |
J. Kočetova, R. Leipus and J. Šiaulys, A property of the renewal counting process with application to the finite-time ruin probability, Lith. Math. J., 49 (2009), 55-61.
doi: 10.1007/s10986-009-9032-1. |
[13] |
R. Leipus and J. Šiaulys, Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes, Insurance Math. Econom., 40 (2007), 498-508.
doi: 10.1016/j.insmatheco.2006.07.006. |
[14] |
R. Leipus and J. Šiaulys, Asymptotic behaviour of the finite-time ruin probability in renewal risk model, Appl. Stoch. Models Bus. Ind., 25 (2009), 309-321.
doi: 10.1002/asmb.747. |
[15] |
J. Li, Q. Tang and R. Wu, Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model, Adv. Appl. Proba., 42 (2010), 1126-1146.
doi: 10.1239/aap/1293113154. |
[16] |
S. I. Resnick, Hidden regular variation, second order regular variation and asymptotic independence, Extrems, 5 (2002), 303-336.
doi: 10.1023/A:1025148622954. |
[17] |
Q. Tang, Asymptotics for the finite time ruin probability in the renewal model with consistent variation, Stoch. Models, 20 (2004), 281-297.
doi: 10.1081/STM-200025739. |
[18] |
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), 109-124.
doi: 10.1007/s11009-011-9226-y. |
[19] |
Y. Wang, Z. Cui, K. Wang and X. Ma, Uniform asymptotics of the finite-time ruin probability for all times, J. Math. Anal. Appl., 390 (2012), 208-223.
doi: 10.1016/j.jmaa.2012.01.025. |
[20] |
Y. Wang, Q. Gao, K. Wang and X. Liu, Random time ruin probability for the renewal risk model with heavy-tailed claims, J. Ind. Manag. Optim., 5 (2009), 719-736.
doi: 10.3934/jimo.2009.5.719. |
[21] |
Y. Yang, R. Leipus, J. Šiaulys and Y. Cang, Uniform estimates for the finite-time ruin probability in the dependent renewal risk model, J. Math. Anal. Appl., 383 (2011), 215-225.
doi: 10.1016/j.jmaa.2011.05.013. |
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