Ruin Probabilities in Compound Renewal Risk Model with Interest Force Under Heavy-tailed Distribution

This paper investigates the finite time ruin probability in compound renewal risk model with interest force under heavy-tailed claims. At first, some important classes of the heavy-tailed distribution are introduced. Considering the situation that in real life, there are often more than one customers asking for claim at the same time. So we discuss the ruin probability in compound renewal risk model instead of renewal risk model. And the surplus process of insurance company with interest force is defined. An asymptotic estimation solution of finite time ruin probability is obtained. The relationship between finite time ruin probability and renewal function is derived. The result provides some theory basis for insurance business to deal with extreme accidence.