Tail asymptotic of discounted aggregate claims with compound dependence under risky investment

References

• Alam, K., and K. M. Lai Saxena. 1981. Positive dependence in multivariate distributions. Communications in Statistics—Theory and Methods 10 (12):1183–96.
   Web of Science ®Google Scholar
• Asmussen, S. 2000. Ruin probabilities. vol. 2. Singapore: World Scientific.
   Google Scholar
• Bingham, N. H., C. M. Goldie, and J. L. Teugels, 1987. Regular variation. Cambridge: Cambridge university press.
   Google Scholar
• Block, H. W., T. H. Savits, M. Shaked, 1982. Some concepts of negative dependence. The Annals of Probability 10 (3):765–72.
   Web of Science ®Google Scholar
• Bowers, N. L., H. U. Gerber, J. C. Hickman, D. A. Jones, and C. J. Nesbitt, 1997. Actuarial mathematics. 2nd edn. The Society of Actuaries: Schaumburg, IL.
   Google Scholar
• Breiman, L. 1965. On some limit theorems similar to the arc-sin law. Theory of Probability and its Applications 10:323–31.
   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
• Cont, R., and P. Tankov, 2004. Financial modelling with jump processes. Boca Raton: Chapman & Hall/CRC.
   Google Scholar
• Ebrahimi, N., and M. Ghosh, 1981. Multivariate negative dependence. Communications in Statistics-Theory and Methods 10:307–37.
   Web of Science ®Google Scholar
• Embrechts, P., C. Klüppelberg, and T. Mikosch, 1997. Modelling extremal events for insurance and finance. Berlin: Springer-Verlag.
   Google Scholar
• Geluk, J., and Q. Tang, 2009. Asymptotic tail probabilities of sums of dependent subexponential random variables. Journal of Theoretical Probability 22:871–82.
   Web of Science ®Google Scholar
• Gerber, H. U. 1982. Ruin theory in the linear model. Insurance: Mathematics and Economics 1:213–17.
   Web of Science ®Google Scholar
• Guo, F., and D. Wang, 2013. Uniform asymptotic estimates for ruin probabilities of renewal risk models with exponential Lévy process investment returns and dependent claims. Applied Stochastic Models in Business and Industry 29 (3):295–313.
   Web of Science ®Google Scholar
• Guo, F., and D. Wang, 2015. Uniform asymptotic estimates for ruin probabilities with exponential Lévy process investment returns and two-sided linear heavy-tailed claims. Communications in Statistics-Theory and Methods 44 (20):4278–306.
   Web of Science ®Google Scholar
• Guo, F., D. Wang, and H. Yang, 2017. Asymptotic results for ruin probability in a two-dimensional risk model with stochastic investment returns. Journal of Computational and Applied Mathematics 325:198–221.
   Web of Science ®Google Scholar
• Joag-Dev, K., and F. Proschan, 1983. Negative association of random variables with applications. The Annals of Statistics 11:286–95.
   Web of Science ®Google Scholar
• Joe, H. 1997. Multivariate Models and Dependence Concepts. London: Chapman & Hall.
   Google Scholar
• Kalashnikov, V., and R. Norberg, 2002. Power tailed ruin probabilities in the presence of risky investments. Stochastic Processes and their Applications 98:211–28.
   Web of Science ®Google Scholar
• Li, J., Q. Tang, and R. Wu, 2010. Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model. Advances in Applied Probability 42:1126–46.
   Web of Science ®Google Scholar
• Maulik, K., and S. Resnick, 2004. Characterizations and examples of hidden regular variation. Extremes 7:31–67.
   Google Scholar
• Paulsen, J. 2002. On Cramèr-like asymptotics for risk processes with stochastic return on investments. The Annals of Applied Probability 12:1247–60.
   Web of Science ®Google Scholar
• Paulsen, J. 2008. Ruin models with investment income. Probability Surveys 5:416–34.
   Google Scholar
• Paulsen, J., and H. K. Gjessing, 1997. Ruin theory with stochastic return on investments. Advances in Applied Probability 29:965–85.
   Web of Science ®Google Scholar
• Peng, J., and J. Huang, 2010. Ruin probability in a one-sided linear model with constant interest rate. Statistics & Probability Letters 80 (7):662–9.
   Web of Science ®Google Scholar
• Sato, K. 1999. Lévy Processes and Infinitely Divisible Distributions. Cambridge: Cambridge University Press.
   Google Scholar
• Stein, C. 1946. A note on cumulative sums. The Annals of Mathematical Statistics 17:498–9.
   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
• Tang, Q., G. Wang, and K. C. Yuen, 2010. Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model. Insurance: Mathematics and Economics 46:362–70.
   Web of Science ®Google Scholar
• Tang, Q., and Z. Yuan, 2012. A hybrid estimate for the finite-time ruin probability in a bivariate autoregressive risk model with application to portfolio optimization. North American Actuarial Journal 16:378–97.
   Google Scholar
• Wang, D., and Q. Tang, 2006. Tail probabilities of randomly weighted sums of random variables with dominated variation. Stochastic models 22:253–72.
   Web of Science ®Google Scholar
• Wang, G., and R. Wu, 2001. Distributions for the risk process with a stochastic return on investments. Stochastic Processes and their Applications 95:329–41.
   Web of Science ®Google Scholar
• Willekens, E. 1987. On the supremum of an infinitely divisible process. Stochastic Processes and their Applications 26:173–5.
   Web of Science ®Google Scholar
• Yang, H., and L. Zhang, 2003. Martingale method for ruin probability in an autoregressive model with constant interest rate. Probability in the Engineering and Informational Sciences 17:183–98.
   Web of Science ®Google Scholar
• Yuen, K. C., G. Wang, and K. W. Ng, 2004. Ruin probabilities for a risk process with stochastic return on investments. Stochastic Processes and their Applications 110:259–74.
   Web of Science ®Google Scholar
• Yuen, K. C., G. Wang, and R. Wu, 2006. On the renewal risk process with stochastic interest. Stochastic Processes and their Applications 116:1496–1510.
   Web of Science ®Google Scholar
• Zhang, Y., X. Shen, and C. Weng, 2009. Approximation of the tail probability of randomly weighted sums and applications. Stochastic processes and their applications 119 (2):655–75.
   Web of Science ®Google Scholar