Study Of The Ruin Proberbility Under Heavy-tail Claims

This thesis is devoted to the study of ruin with heavy-tailed claims, it contains:We use some useful research based on the classic risk model, and obtain a local asymptotic relationship for the survival probability in the renewal risk model under heavy-tailed claims. Then we extend this theorem to the Equilibrium renewal risk model and the Delayed renewal risk model. Discuss and research the Compound renewal risk model under heavy-tailed distribution, obtain a local asymptotic relationship for the survival probability. Then we research the delayed compound renewal risk model and obtain the local asymptotic relationship.The distribution family has carried out extension on heavy tail, discuss the local asymptotic relationship under heavy-tailed distribution in different environment. and obtain a local asymptotic relationship for the ruin probability in the Equilibrium renewal risk model and the Delayed renewal risk model under heavy-tailed claims. After this We push the definition of the heavy-tailed distribution to vague generalization subsequently, and introduce a new heavy-tailed classes with a special renewal risk model, we call it Erlang(n,β) risk model. As we do ,we also obtain a useful conclusion that is the local asymptotic relationship for the Erlang(n,β) risk model. and the delayed model is perfect for this theorem.