汽车保险的簇生点过程模型

The Cluster Point Process Model of Collective Claims in Vehicles Insurance

文章将保险理赔的经典模型——复合泊松过程模型推广,建立簇生点过程模型．以概率母泛函为工具,给出了在(0,t]内理赔总量的均值与方差,并采用鞅分析方法证明了该模型下的Lundberg 不等式．然后将其推广到主过程为重随机过程的情形,得到了平行的结果．

This article generalizes the classical risk model, known as compound Poisson process model, to a new model： cluster point process model. At first, using the probability generating function, the mean and the variance of the sums of claims in （0, t] is given. Secondly, based on the martingale theory, the Lundberg inequality under this model is also proved. Thirdly, we generalize the model to the double stochastic process situation and get a parallel result.