Abstract
In 2007, Chen and Ng investigated infinite-time ruin probability with constant interest force and negatively quadrant dependent and extended regularly varying-tailed claims. Following this work, the authors obtain a weakly asymptotic equivalent formula for the finite-time and infinite-time ruin probability with constant interest force, negatively quadrant dependent, and dominated varying-tailed claims and negatively lower orthant dependent inter-arrival times. In particular, when the claims are consistently varying-tailed, an asymptotic equivalent formula is presented.
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References
Y. Chen and K. W. Ng, The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims, Insurance Mathematics and Economics, 2007, 40(1): 415–423.
Q. Tang, Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation, Scandinavian Actuarial Journal, 2005, 1(1): 1–5.
C. Klüppelberg and U. Stadtimuller, Ruin probability in the presence of heavy-tails and interest rates, Scandinavian Actuarial Journal, 1998, 1(1): 49–58.
S. Asmussen, Subexponential asymptotics for stochastic process: Extremal behavior, stationary distributions and first passage probabilities, Annals of Applied Probability, 1998, 8(2): 354–374.
V. Kalashnikov and D. Konstantinides, Ruin under interest force and subexponential claims: A simple treatment, Insurance Mathematics and Economics, 2000, 27(1): 145–149.
D. Konstantinedes, Q. Tang, and G. Tsitsiashvili, Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails, Insurance Mathematics and Economics, 2002, 31(3): 447–460.
Q. Tang, The finite-time ruin probability of the compound Poisson model with constant interest force, Journal of Applied Probability, 2005, 42(3): 608–619.
E. L. Lehmann, Some concepts of dependence, Annals of Mathematical Statistics, 1966, 37(5): 1137–1153.
H. W. Block, T. H. Savits, and M. Shaked, Some concepts of negative dependence, Annals of Probability, 1982, 10(3): 765–772.
Y. Wang and Y. Yang, The structure and precise moderate deviations of random variables with dominatedly varying tails, Journal of Systems Science and Complexity, 2005, 18(2): 224–232.
P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, New York, 1997.
N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
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 and Their Applications, 2003, 108(2): 299–325.
D. B. H. Cline and G. Samorodnitsky, Subexponentiality of the product of independent random variables, Stochastic Process and Their Applications, 1994, 49(1): 75–98.
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This research is supported by the National Science Foundation of China under Grant No. 10671139.
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Li, J., Wang, K. & Wang, Y. Finite-time ruin probability with NQD dominated varying-tailed claims and NLOD inter-arrival times. J Syst Sci Complex 22, 407–414 (2009). https://doi.org/10.1007/s11424-009-9173-7
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DOI: https://doi.org/10.1007/s11424-009-9173-7