复合二项风险模型中的Z变换

摘要

讨论z变换在风险模型中的应用,先求出复合二项风险模型中一类泛函ψ(u;w),以及特殊情形下ψ(u)和f(u,x)的Z变换,再得出ψ(0)和f(0,x)的表达式,然后求出阶梯高度L1的Z变换,最后在复合二项风险模型索赔个体服从几何分布时,得到其最终生存概率的具体表达式,所得结果与已知结果是相同的.%This paper considers the application of z transform in the risk model. We firstly derive the Z transform of a type of function ψb(u;ω) in the compound binomial risk model. In the two special cases of w(x) ,we get the Z transform of ψ(u) and f(u,x). Applying the value theorem of the Z transform,the explicit expression for ψb(O) and f(O,x) are obtained. Further we get the Z transform of the ladder height L. Finally we obtain the explicit expression of the ultimate survival probability where the individual claim amount distribution is geometric distribution.