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针对经典风险模型中Poisson过程均值必须等于方差这一局限,将其推广到复合Poisson-Geometric过程,并将保费收取次数看作是一个Poisson过程,且每次收到的保费看作是一个随机变量且服从指数分布,得到了对古典风险模型的一个推广.解释了做出这种推广的实际意义,经过推算,得到了调节系数以及破产概率的表达式,进而得到了模型对应的Lundeberg不等式.
In view of the limitation that Poisson process mean must be equal to variance in classical risk model, it is generalized to compound Poisson-Geometric process. The number of premiums is regarded as a Poisson process, and each received premium is regarded as a random variable And obeys the exponential distribution, a generalization of the classical risk model is obtained, and the practical significance of making this kind of extension is explained. Through the calculation, the expression of the adjustment coefficient and the ruin probability is obtained, and the Lundeberg inequality corresponding to the model is obtained.