- Volume 51 Issue 4
This paper studies the asymptotic behavior of the finite-time ruin probability in a jump-diffusion risk model with constant force of interest, upper tail asymptotically independent claims and a general counting arrival process. Particularly, if the claim inter-arrival times follow a certain dependence structure, the obtained result also covers the case of the infinite-time ruin probability.
asymptotics;ruin probability;jump-diffusion model;upper tail asymptotic independence;counting process
- D. Wang, C. Su, and C. Zeng, Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory, Sci. China Ser. A 48 (2005), no. 10, 1379-1394. https://doi.org/10.1360/022004-16
- 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
- Y. Yang and Y. Wang, Asymptotics for ruin probability of some negatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims, Statist. Probab. Lett. 80 (2010), no. 3-4, 143-154. https://doi.org/10.1016/j.spl.2009.09.023
- 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/10.1239/aap/1293113154
- X. Hao and Q. Tang, A uniform asymptotic estimate for discounted aggregate claims with subexponential tails, Insurance Math. Econom. 43 (2008), no. 1, 116-120. https://doi.org/10.1016/j.insmatheco.2008.03.009
- T. Jiang and H. Yan, The finite-time ruin probability for the jump-diffusion model with constant interest force, Acta Math. Appl. Sin. Engl. Ser. 22 (2006), no. 1, 171-176. https://doi.org/10.1007/s10255-005-0295-y
- 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 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.
- 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
- Q. Tang, The ruin probability of a discrete time risk model under constant interest rate with heavy tail, Scand. Actuar. J. 2004 (2004), no. 3, 229-240. https://doi.org/10.1080/03461230310017531
- Q. Tang, Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation, Scand. Actuar. J. 2005 (2005), no. 1, 1-5. https://doi.org/10.1080/03461230510006982
- Q. Tang, Heavy tails of discounted aggregate claims in the continuous-time renewal model, J. Appl. Probab. 44 (2007), no. 2, 285-294. https://doi.org/10.1239/jap/1183667401
- 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
- N. Veraverbeke, Asymptotic estimates for the probability of ruin in a Poisson model with diffusion, Insurance Math. Econom. 13 (1993), no. 1, 57-62. https://doi.org/10.1016/0167-6687(93)90535-W
- D. Wang, Finite-time ruin probability with heavy-tailed claims and constant interest rate, Stoch. Models 24 (2008), no. 1, 41-57. https://doi.org/10.1080/15326340701826898
- N. H. Bingham, C.M. Goldie, and J. L. Teugels, Regular Variation, Cambridge Unversity Press, Cambridge, 1987.
- Y. Chen, L. Wang, and Y. Wang, Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models, J. Math. Anal. Appl. 401 (2013), no. 1, 114-129. https://doi.org/10.1016/j.jmaa.2012.11.046
- Y. Chen and K. 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
- Y. Chen and K. Yuen, Precise large deviations of aggregate claims in a size-dependent renewal risk model, Insurance Math. Econom. 51 (2012), no. 2, 457-461. https://doi.org/10.1016/j.insmatheco.2012.06.010
- Y. Chen, W. Zhang, and J. Liu, Asymptotic tail probability of randomly weighted sum of dependent heavy-tailed random variables, Asia-Pac. J. Risk Insur. 4 (2010), no. 2; http://dx.doi.org/10.2202/2153-3792.1055. Article 4. https://doi.org/10.2202/2153-3792.1055
- D. B. H. Cline and G. Samorodnitsky, Subexponentiality of the product of independent random variables, Stochastic Process. Appl. 49 (1994), no. 1, 75-98. https://doi.org/10.1016/0304-4149(94)90113-9
- P. Embrechts, C. Kluppelberg, and T. Mikosch, Modelling Extremal Events, Springer, Berlin, 1997.
- Q. Gao, N. Jin, and P. Gu, Asymptotic behavior of the finite-time ruin probability with pairwise quasi-asymptotically independent claims and constant interest force, To appear in Rocky Mountain J. Math.; http://projecteuclid.org/euclid.rmjm/1374758577.
- Q. Gao and X. Liu, Uniform asymptotics for the finite-time ruin probability with upper tail asymptotically independent claims and constant force of interest, Statist. Probab. Lett. 83 (2013), no. 6, 1527-1538. https://doi.org/10.1016/j.spl.2013.02.018
- 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
- THE ULTIMATE RUIN PROBABILITY OF A DEPENDENT DELAYED-CLAIM RISK MODEL PERTURBED BY DIFFUSION WITH CONSTANT FORCE OF INTEREST vol.52, pp.3, 2015, https://doi.org/10.4134/BKMS.2015.52.3.895
- Asymptotics for random-time ruin probability in a time-dependent renewal risk model with subexponential claims vol.12, pp.1, 2015, https://doi.org/10.3934/jimo.2016.12.31