带干扰的双广义泊松风险模型

摘要

The classical risk model assumes that the insurance company receives premium at the rate of time constant in per unit time .is a compound Poisson Process in surplus process .This article studies a risk model with the interference item in which both the premium arrival process and the claim counting processes are the generalized homogeneous Poisson processes and meanwhile random disturbance items are added in the model .By the method of Martingale , it puts forward the Lundberg inequality and the formula on the ruin probability based on the model .%经典的风险模型是假定保险公司按单位时间常数速率收取保险费，盈余过程｛ R（t），t ≥0｝中的 S（t）＝∑N（t） Yi 为一复合泊松过程。本文将保费收入过程及索赔过程同时进行推广，即将保费到达过程及索赔计数过程均推广为一广义齐次 P0isson 过程，同时在模型中加入了随机干扰项。应用鞅论的方法，针对此模型给出了 Lundberg 不等式和破产概率公式。