160
Views
0
CrossRef citations to date
0
Altmetric
Articles

Uniform asymptotics for ruin probabilities of multidimensional risk models with stochastic returns and regular variation claims

, &
Pages 6878-6895 | Received 01 Oct 2021, Accepted 21 Jan 2022, Published online: 07 Feb 2022

References

  • Basrak, B.,. R. A. Davis, and T. Mikosch. 2002. Regular variation of GARCH processes. Stochastic Processes and Their Applications 99 (1):95–115. doi:10.1016/S0304-4149(01)00156-9.
  • Bauer, D., and G. Zanjani. 2014. The marginal cost of risk in a multi-period risk model. Technical Report, Robinson College of Business, Georgia State University.
  • Biard, R., C. Lefèvre, and S. Loisel. 2008. Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed. Insurance: Mathematics and Economics 43 (3):412–21. doi:10.1016/j.insmatheco.2008.08.004.
  • Cai, J., D. Landriault, T. Shi, and W. Wei. 2017. Joint insolvency analysis of a shared MAP risk process: A capital allocation application. North American Actuarial Journal 21 (2):178–92. doi:10.1080/10920277.2016.1246254.
  • Cai, J., and H. Li. 2007. Dependence properties and bounds for ruin probabilities in multivariate compound risk models. Journal of Multivariate Analysis 98 (4):757–73. doi:10.1016/j.jmva.2006.06.004.
  • Charpentier, A., and J. Segers. 2009. Tails of multivariate Archimedean copulas. Journal of Multivariate Analysis 100 (7):1521–37. doi:10.1016/j.jmva.2008.12.015.
  • Chen, Y., K. C. Yuen, and K. W. Ng. 2011. Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims. Applied Stochastic Models in Business and Industry 27 (3):290–300. doi:10.1002/asmb.834.
  • Cheng, D., and C. Yu. 2020. Asymptotic ruin probabilities of a two-dimensional renewal risk model with dependent inter-arrival times. Communications in Statistics - Theory and Methods 49 (7):1742–60. doi:10.1080/03610926.2019.1565782.
  • Cheng, D. 2021. Uniform asymptotics for the finite-time ruin probability of a generalized bidimensional risk model with Brownian perturbations. Stochastics 93 (1):56–71. doi:10.1080/17442508.2019.1708362.
  • Collamore, J. F. 1996. Hitting probabilities and large deviations. The Annals of Probability 24 (4):2065–78. doi:10.1214/aop/1041903218.
  • Dhaene, J., A. Tsanakas, E. A. Valdez, and S. Vanduffel. 2012. Optimal capital allocation principles. Journal of Risk and Insurance 79 (1):1–28. doi:10.1111/j.1539-6975.2011.01408.x.
  • Hägele, M. 2020. Precise asymptotics of ruin probabilities for a class of multivariate heavy-tailed distributions. Statistics & Probability Letters 166:108871. doi:10.1016/j.spl.2020.108871.
  • Huang, W., C. Weng, and Y. Zhang. 2014. Multivariate risk models under heavy-tailed risks. Applied Stochastic Models in Business and Industry 30 (3):341–60. doi:10.1002/asmb.1981.
  • Hult, H., and F. Lindskog. 2006a. Heavy-tailed insurance protfolios: Buffer capital and ruin probabilities. Technical Report, vol 1441, School of ORIE, Cornall University.
  • Hult, H., and F. Lindskog. 2006b. On regular variation for infinitely divisible random vectors and additive processes. Advances in Applied Probability 38 (1):134–48. doi:10.1239/aap/1143936144.
  • Hult, H., F. Lindskog, T. Mikosch, and G. Samorodnitsky. 2005. Funtional large deviations for multivariate regularly varying random walks. The Annals of Applied Probability 15 (4):2651–80. doi:10.1214/105051605000000502.
  • Jessen, H. A., and T. Mikosch. 2006. Regularly varying functions. Publications de l’Institut. Publications de L'Institut Mathematique 80 (94):171–92. doi:10.2298/PIM0694171J.
  • Joe, H. 1997. Multivariate models and dependence concepts. New York: Chapman and Hall.
  • Konstantinides, D. G., and J. Li. 2016. Asymptotic ruin probabilities for a multidimensional renewal risk model with multivariate regularly varying claims. Insurance: Mathematics and Economics 69:38–44. doi:10.1016/j.insmatheco.2016.04.003.
  • LeMaire, J. 1984. An application of game theory: Cost allocation. ASTIN Bulletin 14 (1):61–81. doi:10.1017/S0515036100004815.
  • Li, X., J. Wu, and J. Zhuang. 2015. Asymptotic multivariate finite-time ruin probability with statistically dependent heavy-tailed claims. Methodology and Computing in Applied Probability 17 (2):463–77. doi:10.1007/s11009-013-9375-2.
  • Li, J. 2016. Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return. Insurance: Mathematics and Economics 71:195–204. doi:10.1016/j.insmatheco.2016.09.003.
  • Lindskog, F. 2004. Multivariate extremes and regular variation for stochastic processes. Ph. D. Thesis, Department of Mathematics. Swiss Federal Institute of Technology, Switzeland.
  • Picard, P., C. Lefèvre, and I. Coulibaly. 2003. Multirisks model and finite-time ruin probabilities. Methodology and Computing in Applied Probability 5 (3):337–53. doi:10.1023/A:1026287204089.
  • Resnick, S. 1987. Extreme values, regular variation, and point processes. New York: Springer.
  • Resnick, S. I., and E. Willekens. 1991. Moving averages with random coefficients and random coefficient autoregressive models. Comm. Statist. Stochastic Models 7 (4):511–25. doi:10.1080/15326349108807204.
  • Resnick, S. 2007. Heavy-tail phenomena: Probabilistic and statistical modeling. New York: Springer.
  • Samorodnitsky, G., and J. Sun. 2016. Multivariate subexponential distributions and their applications. Extremes 19 (2):171–96. doi:10.1007/s10687-016-0242-8.
  • Shen, X., M. Yuan, and D. Lu. 2020. Ruin problems of multidimensional risk models under constant interest rates and dependent risks with heavy tails. Mathematical Problems in Engineering 2020:1–8. doi:10.1155/2020/9489612.
  • Tang, Q., and Z. Yuan. 2013. Asymptotic analysis of the loss given default in the presence of multivariate regular variation. North American Actuarial Journal 17 (3):253–71. doi:10.1080/10920277.2013.830557.
  • Yang, H., and J. Li. 2014. Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Insurance: Mathematics and Economics 58:185–92. doi:10.1016/j.insmatheco.2014.07.007.
  • Zhang, Y., and W. Wang. 2012. Ruin probabilities of a bidimensional risk model with investment. Statistics & Probability Letters 82 (1):130–8. doi:10.1016/j.spl.2011.09.010.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.