Asymptotic Theory For The Ruin Probabilities Of Renewal Risk Models

In this paper,we study two kinds of non-standard renewal risk models,whose claim size distributions are heavy-tailed.When the initial capital tends to infinity,the asymptotic formulas for the ruin probabilities are investigated.Firstly,we deal with a non-standard renewal risk model with stochastic investment returns.The insurance company is assumed to invest its wealth to the financial market,and the wealth process of its portfolio is described as a geometric Levy process.By further assuming that the claim size distributions belong to the dominated variation class and are also dependent,we will give the asymptotic formula for the tail probability of the discounted aggregate claims.The similar formula for the ruin probability is also derived.Secondly,we consider a by-claim risk model,in which every main claim may be accom?panied with a by-claim occurring after a period of delay.We assume that both the main claims and the by-claims are dominated varying tailed,and they are also pairwise quasi-asymptotically independent.Then the asymptotic formula for the ruin probability is given.