Researches On The Ruin Problems Of Two Types Of Discrete Time Risk Models

In this paper, the rum problems of two types of discrete time risk models are mainly discussed.Firstly, the discrete time risk model with the interest of investment and the rate of inflation is considered. By constructing martingale and using its properties, the paper gets Lundberg inequality of the ultimate ruin probability and the general formulas. Moreover, By using the recursive method, a lot of the 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 and the maximum surplus before ruin, the distribution of deficit at ruin, the joint distribution of surplus before and at ruin and the maximum surplus before ruin are obtained. In addition, the distribution of the time when the surplus process reaches a given level for the first time is obtained.Secondly, the classical discrete time risk model, namely, the compound binomial risk model is further discussed. Using the notion of martingale, the paper obtains the ultimate ruin probability and the distributions of the first and the last arrival time of a given level.