DOI QR코드

DOI QR Code

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 (School of Mathematics and Statistics Nanjing Audit University) ;
  • Yang, Yang (School of Mathematics and Statistics Nanjing Audit University)
  • 투고 : 2011.12.04
  • 발행 : 2013.03.31

초록

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.

키워드

참고문헌

  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. https://doi.org/10.1080/15326340802641006
  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. https://doi.org/10.1016/j.insmatheco.2008.03.009
  5. H. Jasiulewicz, Probability of ruin with variable premium rate in a Markovian environment, Insurance Math. Econom. 29 (2001), no. 2, 291-296. https://doi.org/10.1016/S0167-6687(01)00090-7
  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. https://doi.org/10.1016/j.spl.2008.05.036
  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. https://doi.org/10.2143/AST.26.1.563235
  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. https://doi.org/10.1016/j.spa.2003.07.001
  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. https://doi.org/10.1023/B:EXTR.0000031178.19509.57
  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. https://doi.org/10.1080/03461230510006982
  13. Q. Tang, Heavy tails of discounted aggregate claims in the continous-time renewal model, J. Appl. Probab. 44 (2007), no. 2, 285-294. https://doi.org/10.1239/jap/1183667401
  14. 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
  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. https://doi.org/10.1007/s11009-011-9226-y
  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. https://doi.org/10.1016/j.spl.2009.09.023
  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. https://doi.org/10.1016/j.jmaa.2010.10.020

피인용 문헌

  1. Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest vol.419, pp.2, 2014, https://doi.org/10.1016/j.jmaa.2014.05.069
  2. 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
  3. 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