Asymptotic Properties Based On Customer-Arrival Risk Model With Dependent Claims

As we all know, risk model is the foundation of Finance and Actuarial Science and the core problem of the risk theory is the study of the theory of bankruptcy. The ruin theory, are more concerned by some important events. Because the significant event probability is very small and difficult extremely to predict, but once happened, it will bring great loss, resulting in large claims, the insurance company’s business will be bringed huge risk. In the course of the study, heavy tailed distribution is more consistent than the light tailed distribution. Recently, the trend in risk research model heavy-tailed claim amount is a variety of risk dependency structure model, so that make the insurance company’s operations fit. In the theory of risk, the asymptotic for ruin probabilities are related to the research of large deviation theory. Therefore, the study of large deviations theory has become one of the important issues concerned by scholars. In this paper, under the conditions of heavy-tailed distributions, the precise large deviations based on customer-arrival risk model and asymptotic of the ruin probability based on entrance process are discussed.The content of this paper includes the following four chapters:In chapter1, we introduce the research history and the development status of ruin the-ory, the relevant knowledge of the heavy tailed distributions and the dependence structure, besides, we summarize the various generalizations of the classical risk model.In chapter2, we introduce the risk model based on the customer arrival, in which claim size is described as indicator function, so that the amount of claim to be more accu-rately expressed. Under the assumption that claim sizes random variables are negatively dependent, identically distributed and belonged to class C∩D, we study the precise large deviation result both the partial sums and the random sums.In chapter3, we discuss the special case based on the customer-arrival in which is based on entrance process. And generalize the result, the claim of the model sequences are pairwise quasi-asymptotically independent and belonged to class D. We obtain an asymptotical equality expression of the finite time ruin probability. In chapter4, we summarize this paper and the prospect further research work.