Large deviations for the stochastic present value of aggregate claims in the nonstandard compound renewal risk model with widely upper Orthant dependent claims

References

• Bingham, N. H., C. M. Goldie, and J. L. Teugels. 1987. Regular variation. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Chen, Y., K. C. Yuen, and K. W. Ng. 2011. Precise large deviations of random sums in presence of negative dependence and consistent variation. Methodology and Computing in Applied Probability 13 (4):821–33. doi:10.1007/s11009-010-9194-7.
   Web of Science ®Google Scholar
• Chen, Y., and K. C. Yuen. 2012. Precise large deviations of aggregate claims in a size-dependent renewal risk model. Insurance: Mathematics and Economics 51 (2):457–61. doi:10.1016/j.insmatheco.2012.06.010.
   Web of Science ®Google Scholar
• Cline, D. B. H., and G. Samorodnitsky. 1994. Subexponentiality of the product of independent random raviables. Stochastic Processes and Their Applications 49 (1):75–98. doi:10.1016/0304-4149(94)90113-9.
   Web of Science ®Google Scholar
• Cont, R., and P. Tankov. 2004. Financial modelling with jump processes. Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Dong, Y., and Y. Wang. 2011. Uniform estimates for ruin probabilities in the renewal risk model with upper-tail independent claims and premiums. Journal of Industrial and Management Optimization 7 (4):849–74. doi:10.3934/jimo.2011.7.849.
   Web of Science ®Google Scholar
• Embrechts, P., C. Klüppelberg, and T. Mikosch. 1997. Modelling extremal events for insurance and finance. Berlin, Germany: Springer.
   Google Scholar
• He, W., D. Cheng, and Y. Wang. 2013. Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables. Statistics & Probability Letters 83 (1):331–8. doi:10.1016/j.spl.2012.09.019.
   Web of Science ®Google Scholar
• Jiang, T., S. Cui, and R. Ming. 2015. Large deviations for the stochastic present value of aggregate claims in the renewal risk model. Statistics & Probability Letters 101 :83–91. doi:10.1016/j.spl.2015.02.020.
   Web of Science ®Google Scholar
• Kalashnikov, V., and R. Norberg. 2002. Power tailed ruin probabilities in the presence of risky investments. Stochastic Processes and Their Applications 98 (2):211–28. doi:10.1016/S0304-4149(01)00148-X.
   Web of Science ®Google Scholar
• Klüppelberg, C., and R. Kostadinova. 2008. Integrated insurance risk models with exponential Lévy investment. Insurance: Mathematics and Economics 42 (2):560–77. doi:10.1016/j.insmatheco.2007.06.002.
   Web of Science ®Google Scholar
• Liu, L. 2009. Precise large deviations for dependent variables with heavy tails. Statistics & Probability Letters 79 (9):1290–8. doi:10.1016/j.spl.2009.02.001.
   Web of Science ®Google Scholar
• Liu, X., C. Yu, and Q. Gao. 2017. Precise large deviations of aggregate claim amount in a dependent renewal risk model. Communications in Statistics - Theory and Methods 46(5):2354–63. doi:10.1080/03610926.2015.1044666.
   Web of Science ®Google Scholar
• McNeil, A., R. Frey, and P. Embrechts. 2005. Quantitative risk management. Princeton, NJ: Princeton University Press.
   Google Scholar
• Paulsen, J., and H. K. Gjessing. 1997. Ruin theory with stochastic return on investments. Advances in Applied Probability 29 (04):965–85. doi:10.1017/S0001867800047972.
   Web of Science ®Google Scholar
• Tang, Q., and G. Tsitsiashvili. 2003. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Processes and Their Applications 108 (2):299–325. doi:10.1016/j.spa.2003.07.001.
   Web of Science ®Google Scholar
• Tang, Q. 2006. Insensitivity to negative dependence of the asymptotic behavior of precise large deviations. Electronic Journal of Probability 11 (0):107–20. doi:10.1214/EJP.v11-304.
   Web of Science ®Google Scholar
• Tang, Q., G. Wang, and K. Yuen. 2010. Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model. Insurance: Mathematics and Economics 46 (2):362–70. doi:10.1016/j.insmatheco.2009.12.002.
   Web of Science ®Google Scholar
• Wang, K., Y. Yang, and J. Lin. 2012. Precise large deviations for widely orthant dependent random variables with dominatedly varying tails. Frontiers of Mathematics in China 7 (5):919–32. doi:10.1007/s11464-012-0227-0.
   Web of Science ®Google Scholar
• Wang, K., Y. Wang, and Q. Gao. 2013. Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate. Methodology and Computing in Applied Probability 15 (1):109–24. doi:10.1007/s11009-011-9226-y.
   Web of Science ®Google Scholar
• Xiao, M., S. Cui, R. Ming, and T. Jiang. 2017. Large deviations for the stochastic present value of aggregate net claims with infinite variance in the renewal risk model and its application in risk management. Cluster Computing 21: 997–1007. doi:10.1007/s10586-017-1007-0.
   Web of Science ®Google Scholar
• Yang, Y.,. R. Leipus, and J. Šiaulys. 2012. Precise large deviations for compound random sums in the presence of dependence structures. Computers & Mathematics with Applications 64:2074–83. doi:10.1016/j.camwa.2012.04.003.
   Web of Science ®Google Scholar