| 复合二项风险模型中的Z变换 |
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| 引用本文： | 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. |
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| 作者姓名： | 方世祖 刘果 文厚明 |
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| 作者单位： | 广西大学数学与信息科学学院,广西南宁,530004 |
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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.
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| 关 键 词： | 复合二项风险模型 Z变换 破产概率 终值定理 |
| 收稿时间： | 2010/7/20 0:00:00 |
| 修稿时间： | 2010/10/15 0:00:00 |
Z Transform in the Compound Binomial Risk Model |
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| FANG Shi-zu,LIU Guo and WENG Hou-ming.Z Transform in the Compound Binomial Risk Model[J].Guangxi Sciences,2011,18(1):30-33. |
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| Authors: | FANG Shi-zu LIU Guo and WENG Hou-ming |
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| Institution: | FANG Shi-zu,LIU Guo,WENG Hou-ming(College of Mathematics and Information Science,Guangxi University,Nanning,Guangxi,530004,China) |
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| 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. |
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| Keywords: | compound binomial risk model Z transform ruin probability value theorem |
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