Ruin Probability For An Autoregressive Risk Model With Different Times Of Insurance Business

In actuarial science,the classical models are usually based on the independency assumption, that is,the premiums and claims are assumed to be two independent and identically distributed(iid) randon variables series, and different times of policies are independent of each other.However ,these assumptions may not be justified in many real situations. In rencent years ,risk models with dependence structuces have been studied by many researchers.In this paper, the dependent insurance business is considered. We assume that the vector process of premiums and claims is described by a multivarite autoregressive model of order p(MAR(p)).We study ruin probabilities in two situations ,one is that there is only one time of insurance business,another is that there are two dependent times of business. A constant rate is also included in the model. If there are two times of business ,we also consider the ruin probabilities and define some differnet joint ruin probabilities.The ruin probabilities are derived by using martingale inequalities.In the last chapter of this article, some of the numerical examples are given to show the usefulness of the upper bounds obtained in this paper and relationship between the parameters in the model and the ruin probabilities.This paper is an extension of Zhang and Yuen (2004).The difference is that this paper conside the vector process of premiums and claims is described by a multivarite autoregressive model and also conside some different ruin probabilities.The model studied in this paper i have founded is useful not only in theory but also in practice. It can be used by an insurance company to adjust its initial surplues of all times of business,until the ruin probablities of the company and every times of business are acceptable .