Research On Compound Negative Binomial Risk Model

In this paper, the ruin problems of several types of discrete risk model are mainly discussed.Firstly, the claim number is generalized to a negative stochastic series, and compound negative risk model is given. By the properties of compound negative stochastic series, the survival probability is got when the initial capital is zero. "The paper also gets survival probability in finite time, ultimate ruin probability and Lundberg inequality. Furthermore, it obtains the distributions of the time that surplus reaches a given level for the first and the last time . Secondly, the compound negative risk model is generalized to the double compound negative risk model, by using the recursive method, a lot of theoretical problems are resolved, such as the distributions of the ruin time and the ruin lasting time, the ruin probability in finite time, the ultimate ruin probability. Furthermore, in this paper, the distributions of the surplus before ruin are obtained. Thirdly, a discrete insurance risk model of two-type claims is considered, the properties of surplus, the ultimate ruin probability and Lundberg inequality are got. Lastly, the paper also studies on a generalized discrete insurance risk model of two-type claims, the problems are resolved, such as the survival probability, ruin probability when the initial capital is zero and the ultimate ruin probability.