Abstract
We consider a nonstandard risk model with constant interest rate. For the case where the claim sizes follow a common heavy-tailed distribution and fulfill a dependence structure proposed by Geluk and Tang [J. Geluk and Q. Tang, Asymptotic tail probabilities of sums of dependent subexponential random variables, J. Theor. Probab., 22:871–882, 2009] while the interarrival times fulfill the so-called widely lower orthant dependence, we establish a weakly asymptotically equivalent formula for the infinite-time ruin probability. In particular, when the dependence structure for claim sizes is strengthened to the widely upper orthant dependence, this result implies a uniformly asymptotically equivalent formula for the finite-time and infinite-time ruin probabilities.
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This work was supported by the National Natural Science Foundation of China (No. 11001052), China Postdoctoral Science Foundation (No. 20100471365), Natural Science Foundation of Jiangsu Province of China (No. BK2010480), Postdoctoral Research Program of Jiangsu Province of China (No. 0901029 C), Jiangsu Government Scholarship for Overseas Studies, Qing Lan Project.
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Yang, Y., Wang, K. Uniform asymptotics for the finite-time and infinite-time ruin probabilities in a dependent risk model with constant interest rate and heavy-tailed claims. Lith Math J 52, 111–121 (2012). https://doi.org/10.1007/s10986-012-9159-3
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DOI: https://doi.org/10.1007/s10986-012-9159-3