Approximation of the Tail Probability of Dependent Random Sums Under Consistent Variation and Applications

作者：Lin, Zhengyan; Shen, Xinmei^*

来源：Methodology and Computing in Applied Probability, 2013, 15(1): 165-186.

DOI：10.1007/s11009-011-9232-0

• Compound renewal risk model
• Ruin probability
• Consistent variation
• Asymptotically quadrant sub-independent
• Markov environment process

In this paper, we consider the random sums of one type of asymptotically quadrant sub-independent and identically distributed random variables {X, X (i) , i = 1, 2, a <-aEuro parts per thousand} with consistently varying tails. We obtain the asymptotic behavior of the tail under different cases of the interrelationships between the tails of X and eta, where eta is an integer-valued random variable independent of {X, X (i) , i = 1, 2, a <-aEuro parts per thousand}. We find out that the asymptotic behavior of is insensitive to the dependence assumed in the present paper. We state some applications of the asymptotic results to ruin probabilities in the compound renewal risk model under dependent risks. We also state some applications to a compound collective risk model under the Markov environment.

• 出版日期2013-3
• 单位大连理工大学; 浙江大学