Several Types Of Dual Risk Model With Dependent Bankruptcy Research

The classical Cramer-Lundberg risk model has been promoted by many people since it was proposed. While they are based on the independent assumptions, these are, the counting process in different types of insurance claims is independent of each other; counting process claims and premiums arrived at the counting process are assumed to be independent. In other words, the claims of different kinds of insurance are independent and the premiums and claims are assumed to be two indepe-ndent and identically distributed(iid) random variables series, anddifferent times of polices are independent of each other. In the managemen of the insurance company, because of economic impact of competition, interestrate, inflation rate and random interferemces, the counting processes in different types of insurance claims are dependent, counting process claims and premiums arrived at the counting process are also dependent. There is necessary for this type of grow situation to provide more objective and actual risk model nearly. In this thesis we build up and discuss several kinds of dependent double-type risk models:(1) We study a correlated aggregate claims model,in which the arrival of the income of premium is a compound poisson process with constant interest and inflation rate.First we convert the two correlated aggregate claims to independent aggregate claims. Then we get Lundberg inequality by using martingle theory.(2) We consider the Probability properties of a double-type risk model in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a poisson process and the process of claim occurring is thinning process. A integral equation for the survival probability is obtained. The explicit expression of the survival probability for the infinite interval is obtained in the special case of exponential distribution.(3) We study the ruin probability problem of the double-type risk model perturbed in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is thinning process. Using martingale method, the lundberg inequality and the common formula for the ruin probability are proved.