JOURNAL BROWSE
Search
Advanced SearchSearch Tips
UNIFORM ASYMPTOTICS FOR THE FINITE-TIME RUIN PROBABILITY IN A GENERAL RISK MODEL WITH PAIRWISE QUASI-ASYMPTOTICALLY INDEPENDENT CLAIMS AND CONSTANT INTEREST FORCE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
UNIFORM ASYMPTOTICS FOR THE FINITE-TIME RUIN PROBABILITY IN A GENERAL RISK MODEL WITH PAIRWISE QUASI-ASYMPTOTICALLY INDEPENDENT CLAIMS AND CONSTANT INTEREST FORCE
Gao, Qingwu; Yang, Yang;
  PDF(new window)
 Abstract
In the paper we study the finite-time ruin probability in a general risk model with constant interest force, in which the claim sizes are pairwise quasi-asymptotically independent and arrive according to an arbitrary counting process, and the premium process is a general stochastic process. For the case that the claim-size distribution belongs to the consistent variation class, we obtain an asymptotic formula for the finite-time ruin probability, which holds uniformly for all time horizons varying in a relevant infinite interval. The obtained result also includes an asymptotic formula for the infinite-time ruin probability.
 Keywords
uniform;asymptotics;finite-time;ruin;probability;pairwise;quasiasymptotic;independence;consistent;variation;
 Language
English
 Cited by
1.
THE ULTIMATE RUIN PROBABILITY OF A DEPENDENT DELAYED-CLAIM RISK MODEL PERTURBED BY DIFFUSION WITH CONSTANT FORCE OF INTEREST,;;;

대한수학회보, 2015. vol.52. 3, pp.895-906 crossref(new window)
1.
Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest, Journal of Mathematical Analysis and Applications, 2014, 419, 2, 1193  crossref(new windwow)
2.
Asymptotics for random-time ruin probability in a time-dependent renewal risk model with subexponential claims, Journal of Industrial and Management Optimization, 2015, 12, 1, 31  crossref(new windwow)
3.
THE ULTIMATE RUIN PROBABILITY OF A DEPENDENT DELAYED-CLAIM RISK MODEL PERTURBED BY DIFFUSION WITH CONSTANT FORCE OF INTEREST, Bulletin of the Korean Mathematical Society, 2015, 52, 3, 895  crossref(new windwow)
 References
1.
N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.

2.
Y. Chen and K. Yuen, Sums of pairwise quasi-asymptotically independent random variables with consistent variation, Stoch. Models 25 (2009), no. 1, 76-89. crossref(new window)

3.
P. Embrechts, C. Kluuppelberg, and T. Mikosch, Modelling Extremal Events, For Insurance and Finance, Springer, Berlin, 1997.

4.
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. crossref(new window)

5.
H. Jasiulewicz, Probability of ruin with variable premium rate in a Markovian environment, Insurance Math. Econom. 29 (2001), no. 2, 291-296. crossref(new window)

6.
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. crossref(new window)

7.
S. Kotz, N. Balakrishnan, and N. L. Johnson, Continuous Multivariate Distributions. Vol. 1, Models and applications. Second edition. Wiley Series in Probability and Statistics: Applied Probability and Statistics. Wiley-Interscience, New York, 2000.

8.
F. Michaud, Estimating the probability of ruin for variable premiums by simulation, Astin Bull. 26 (1996), no. 1, 93-105. crossref(new window)

9.
S. S. Petersen, Calculation of ruin probabilities when the premium depends on the current reserve, Scand. Actuar. J. 1898 (1989), no. 3, 147-159.

10.
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. crossref(new window)

11.
Q. Tang and G. Tsitsiashvili, Randomly weighted sums of subexponential random variables with application to ruin theory, Extremes 6 (2003), no. 3, 171-188. crossref(new window)

12.
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. crossref(new window)

13.
Q. Tang, Heavy tails of discounted aggregate claims in the continous-time renewal model, J. Appl. Probab. 44 (2007), no. 2, 285-294. crossref(new window)

14.
D. Wang, Finite-time ruin probability with heavy-tailed claims and constant interest rate, Stoch. Models 24 (2008), no. 1, 41-57. crossref(new window)

15.
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. crossref(new window)

16.
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. crossref(new window)

17.
L. Yi, Y. Chen, and C. Su, Approximation of the tail probability of randomly weighted sums of dependent random variables with dominated variation, J. Math. Anal. Appl. 376 (2011), no. 1, 365-372. crossref(new window)