| 引用本文： |
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方世祖,刘果,文厚明.复合二项风险模型中的Z变换[J].广西科学,2011,18(1):30-33. [点击复制]
- FANG Shi-zu,LIU Guo,WENG Hou-ming.Z Transform in the Compound Binomial Risk Model[J].Guangxi Sciences,2011,18(1):30-33. [点击复制]
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| 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Li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. |
| 关键词: 复合二项风险模型 Z变换 破产概率 终值定理 |
| DOI： |
| 投稿时间：2010-07-20修订日期：2010-10-15 |
| 基金项目: |
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| Z Transform in the Compound Binomial Risk Model |
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FANG Shi-zu, LIU Guo, WENG Hou-ming
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| (College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| This paper considers the application of z transform in the risk model.We firstly derive the Z transform of a type of function ψ (u;w) 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 ψ (0) and f (0, x) are obtained.Further we get the Z transform of the ladder height Li.Finally we obtain the explicit expression of the ultimate survival probability where the individual claim amount distribution is geometric distribution. |
| Key words: compound binomial risk model Z transform ruin probability value theorem |
