Survival Probability in a Risk Model Under Heavy-tailed Claims

In this paper,the authors establish a generalized renewal risk model based on the reality that unexpected heavy- tailedclaims is one of important factors which result in ruin of the insurance companies,and obtain local asymptotic relationship of survival probabilities and tailequivalence relationship for the ruin probabilities under the assumption that the claims size is heavy- tailedF∈S~*.The results are uniform as that in the Cramer-Lundberg model and have their uniqueness either,and significantly extend and improve many known results.