The Expansion And Application Of Convolution Of Dfs With 2-nd Order And N-th Order General Regular Variation Tail

In this paper, we research the high order expansion of heavy tail dfs. Firstly, the convolution expansion of dfs with 2-th order and n-th general regular variation tail are investigated. Under the assumptions of general regular variation tail, we obtain the n-th orderexpansion of convolution F*G and prove the convolution closure of dfs. Next, these results are applied to the Cramer-Lundberg model and 2-nd order, 3-rd order, n-th order expansion are obtained.