模糊风险变量相依性的非参数度量及在保险中的应用

发布时间：2018-08-26 15:49

【摘要】：本文从分布函数与样本观测值数据两方面探讨模糊随机变量的相依性。若已知模糊随机变量左右端点值分布函数，通过copula函数理论从分布函数建立模糊copula函数模型求出模糊随机变量的联合分布函数；若无法已知模糊随机变量的分布函数，，以kendall统计量为基础，从一致相依性角度对二模糊随机变量进行相依性度量。通过模糊排序方法提出模糊一致相依性度量参数；证明Kendall统计量是相依性度量参数的一个无偏估计。建立模糊kendall统计量作为模糊随机变量之间的相依性度量工具。最后通过模糊随机变量的相依性度量工具探讨保险业务中个体风险和聚合风险模型。
[Abstract]:In this paper, the dependence of fuzzy random variables is discussed in terms of distribution function and sample observation data. If the distribution function of left and right endpoints of fuzzy random variables is known, the joint distribution function of fuzzy random variables can be obtained from the model of fuzzy copula function by copula function theory, if the distribution function of fuzzy random variables cannot be known, Based on kendall statistics, this paper measures the dependence of two fuzzy random variables from the point of view of uniform dependence. The fuzzy uniform dependency metric parameter is proposed by fuzzy sorting method, and it is proved that the Kendall statistic is an unbiased estimate of the dependency metric parameter. A fuzzy kendall statistic is established as a tool for measuring the dependence of fuzzy random variables. Finally, the model of individual risk and aggregate risk in insurance business is discussed by means of the dependency measurement tool of fuzzy random variables.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O211.5;F840

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