Survival probability and ruin probability of a risk model

摘要

In this paper,a new risk model is studied 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 p-thinning process.The integral representations of the survival probability are gotten.The explicit formula of the survival probability on the infinite interval is obtained in the special case-exponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.