The Subexponential Distribution wthin Renewal Model

Abstract

Here, we investigate asymptotic equivalent formulas for finite-time ruin probabilities in a renewal risk model with a subexponential distribution in this research, in the cases of the negatively dependent and upper tail independent, respectively. First, we extend the related research results of Tao Jiang, and Chengguo Weng et al. to the subexponential case, respectively. Thereafter two precise asymptotic equivalent relations are established, one is the finite-time probability when the random variables of the claims are influenced by the common subexponential distribution in a negative way, and another the finite-time ruin probability when the claimsizes are upper tail independent with the common subexponential distribution.