短期个别风险模型与短期聚合风险模型关系

本文证明了短期个别风险模型当理赔次数随机变量为0-1分布时,可以寻求一个短期聚合风险模型与之等价;更为重要的,当个别风险模型的索赔次数随机变量服从较小参数的Poisson分布时,也可以寻求到一个复合Poisson分布与之近似。为此,本文解决了一些特定风险损失随机变量和的分布计算问题,Panjer迭代是其计算基础。

It is proved that the short-term Individual Risk Models are equivalent to the short-term Collective Risk Models when the number-of-claim random variable has 0-1 distribution. Furthermore, the Individual Risk Model is close to a compound Poisson distribution if the number-of-claim random variable has a Poisson distribution with small parameter. Based on the Panjer Iteration, the problem of calculating distribution of random variable of aggregate claims is solved.