Asymptotic ruin probabilities for a bidimensional risk model with heavy-tailed claims and non-stationary arrivals

References

• Bordenave, C., and G. L. Torrisi. 2007. Large deviations of Poisson cluster processes. Stochastic Models 23:593–625.
   Web of Science ®Google Scholar
• Chan, W., H. Yang, and L. Zhang. 2003. Some results on ruin probabilities in a two-dimensional risk model. Insurance: Mathematics and Economics 32:345–58.
   Web of Science ®Google Scholar
• Chen, Y., Y. Wang, and K. Wang. 2013. Asymptotic results for ruin probability of a two-dimensional renewal risk model. Stochastic Analysis and Applications 31:80–91.
   Web of Science ®Google Scholar
• 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 27:290–300.
   Web of Science ®Google Scholar
• Cline, D. B. H. 1994. Intermediate regular and Π-variation. Proceedings of the London Mathematical Society 68:594–616.
   Web of Science ®Google Scholar
• Cline, D. B. H., and G. Samorodnitsky. 1994. Subexponentiality of the product of independent random variables. Stochastic Processes and their Applications 49:75–98.
   Web of Science ®Google Scholar
• Daley, D. J. and D. Vere-Jones, 2003. An introduction to the theory of point processes. Vols. 1and2, 2nd ed. New York: Springer.
   Google Scholar
• Dembo, A., Zeitouni, O. 1998. Large deviations techniques and applications. 2nd ed. New York: Springer.
   Google Scholar
• Gao, Q. and X. Yang. 2014. Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest. Journal of Mathematical Analysis and Applications 419:1193–213.
   Web of Science ®Google Scholar
• Hawkes, A. G. 1971. Spectra of some self-exciting and mutually exciting point processes. Biometrika 58:83–90.
   Web of Science ®Google Scholar
• Jiang, H., S. Li, and S. Wang. 2017. Deviation inequalities, moderate deviation principles for certain Gaussian functionals, and their applications in parameter estimation. Stochastic Analysis and Applications 35 (4):615–32.
   Web of Science ®Google Scholar
• Karabash, D., and L. Zhu. 2015. Limit theorems for marked Hawkes processes with application to a risk model. Stochastic Models 31:433–51.
   Web of Science ®Google Scholar
• Lefevere, R., M. Mariani, and L. Zambotti. 2011. Large deviations for renewal processes. Stochastic Processes and their Applications 121 (10):2243–71.
   Web of Science ®Google Scholar
• Li, J., Z. Liu, and Q. Tang. 2007. On the ruin probabilities of a bidimensional perturbed risk model. Insurance: Mathematics and Economics 41:185–95.
   Web of Science ®Google Scholar
• Li, J., and H. Yang. 2015. Asymptotic ruin probabilities for a bidimensional renewal risk model with constant interest rate and dependent claims. Journal of Mathematical Analysis and Applications 426:247–66.
   Web of Science ®Google Scholar
• Liu, X., Q. Gao, and E. Guo. 2016. Uniform asymptotics for ruin probability of a two-dimensional dependent renewal risk model. Communication in Statistics—Theory and Methods 45:6045–60.
   Web of Science ®Google Scholar
• Macci, C., and B. Pacchiarotti. 2015. Large deviations for a class of counting processes and some statistical applications. Statistics & Probability Letters 104:36–48.
   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 108:299–325.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Zhang, Y., and W. Wang. 2012. Ruin probabilities of a bidimensional risk model with investment. Statistics & Probability Letters 82:130–8.
   Web of Science ®Google Scholar
• Zhu, L. 2013a. Moderate deviations for Hawkes processes. Statistics & Probability Letters 83:885–90.
   Web of Science ®Google Scholar
• Zhu, L. 2013b. Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims. Insurance: Mathematics and Economics 53:544–50.
   Web of Science ®Google Scholar