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Uniform asymptotics of the finite-time ruin probability for all times. (English) Zbl 1237.91139

The study focuses on the uniform asymptotic behavior of the finite-time ruin probability, within a risk framework which provides advancements about the hypotheses involving claim sizes.

In particular, the authors consider independent strong subexponential claim sizes and widely lower orthant dependent inter-occurrence times. Within this renewal model the asymptotics of the finite-time ruin probability are investigated.

MSC:
91B30Risk theory, insurance
60K10Applications of renewal theory
References:
[1]Block, H. W.; Savits, T. H.; Shaked, M.: Some concepts of negative dependence, Ann. probab. 10, 765-772 (1982) · Zbl 0501.62037 · doi:10.1214/aop/1176993784
[2]Chistyakov, V. P.: A theorem on sums of independent positive random variables and its applications to branching process, Theory probab. Appl. 9, 640-648 (1964) · Zbl 0203.19401
[3]Cline, D. B. H.; Samorodnitsky, G.: Subexponentiality of the product of independent random variables, Stochastic process. Appl. 49, 75-98 (1994) · Zbl 0799.60015 · doi:10.1016/0304-4149(94)90113-9
[4]Denisov, D.; Foss, S.; Korshunov, D.: Tail asymptotics for the supremum of a random walk when the mean is not finite, Queueing syst. 46, 15-33 (2004) · Zbl 1056.90028 · doi:10.1023/B:QUES.0000021140.87161.9c
[5]Ebrahimi, N.; Ghosh, M.: Multivariate negative dependence, Comm. statist. Theory methods 10, 307-337 (1981) · Zbl 0506.62034
[6]Embrechts, P.; Klüppelberg, C.; Mikosch, T.: Modelling extremal events for insurance and finance, (1997)
[7]Jiang, T.: Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities, Sci. China ser. A 51, 1257-1265 (2008) · Zbl 1149.91037 · doi:10.1007/s11425-008-0083-2
[8]Klüppelberg, C.: Subexponential distributions and integrated tails, J. appl. Probab. 25, 132-141 (1988) · Zbl 0651.60020 · doi:10.2307/3214240
[9]Kočetova, J.; Leipus, R.; Šiaulys, J.: A property of the renewal counting process with application to the finite-time ruin probability, Lith. math. J. 49, 55-61 (2009) · Zbl 1185.60098 · doi:10.1007/s10986-009-9032-1
[10]Korshunov, D.: Large-deviation probabilities for maxima of sums of independent random variables with negative mean and subexponential distribution, Theory probab. Appl. 46, 355-366 (2002) · Zbl 1005.60060 · doi:10.1137/S0040585X97979019
[11]Leipus, R.; Šiaulys, J.: Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes, Insurance math. Econom. 40, 498-508 (2007) · Zbl 1183.91073 · doi:10.1016/j.insmatheco.2006.07.006
[12]Leipus, R.; Šiaulys, J.: Asymptotic behaviour of the finite-time ruin probability in renewal risk model, Appl. stoch. Models bus. Ind. 25, 309-321 (2009) · Zbl 1224.91070 · doi:10.1002/asmb.747
[13]Liu, L.: Precise large deviations for dependent random variables with heavy tails, Statist. probab. Lett. 79, 1290-1298 (2009) · Zbl 1163.60012 · doi:10.1016/j.spl.2009.02.001
[14]Matula, P.: A note on the almost sure convergence of sums of negatively dependent random variables, Statist. probab. Lett. 15, 209-213 (1992) · Zbl 0925.60024 · doi:10.1016/0167-7152(92)90191-7
[15]Sgibnev, M. S.: Submultiplicative moments of the supremum of a random walk with negative drift, Statist. probab. Lett. 32, 377-383 (1997) · Zbl 0903.60055 · doi:10.1016/S0167-7152(96)00097-1
[16]Tang, Q. H.: Asymptotics for the finite time ruin probability in the renewal model with consistent variation, Stoch. models 20, 281-297 (2004) · Zbl 1130.60312 · doi:10.1081/STM-200025739
[17]Tang, Q. H.: Uniform estimates for the tail probability of maxima over finite horizons with subexponential tails, Probab. engrg. Inform. sci. 18, 71-86 (2004) · Zbl 1040.60038 · doi:10.1017/S0269964804181059
[18]Wang, K.; Wang, Y.; Gao, Q.: Uniform asymptotics for the finite-time ruin probability of a new dependent risk model with a constant interest rate, Methodol. comput. Appl. probab. (2010)
[19]Wang, Y.; Cheng, D.: Basic renewal theorems for a random walk with widely dependent increments and their applications, J. math. Anal. appl. 384, 597-606 (2011) · Zbl 1230.60095 · doi:10.1016/j.jmaa.2011.06.010
[20]Wang, Y.; Wang, K.: Random walks with non-convolution equivalent increments and their applications, J. math. Anal. appl. 374, 88-105 (2011) · Zbl 1214.60016 · doi:10.1016/j.jmaa.2010.08.040
[21]Wang, Y.; Yang, Y.; Wang, K.; Cheng, D.: Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications, Insurance math. Econom. 40, 256-266 (2007) · Zbl 1120.60033 · doi:10.1016/j.insmatheco.2006.04.006
[22]Yang, Y.; Leipus, R.; Šiaulys, J.; Cang, Y.: Uniform estimates for the finite-time ruin probability in the dependent renewal risk model, J. math. Anal. appl. 383, 215-225 (2011) · Zbl 1229.91169 · doi:10.1016/j.jmaa.2011.05.013