平衡损失函数下对信度理论的进一步研究

发布时间：2018-02-26 18:16

本文关键词： 信度原理平衡损失函数指数保费原理通货膨胀因子相依结构　出处：《新疆大学》2013年硕士论文　论文类型：学位论文

【摘要】：平衡损失函数既反映了估计的精确性,又反映了拟合程度的好坏.它已成为许多领域的研究课题,所以本文在平衡损失函数下对信度理论作了进一步研究. 首先,在经典信度理论中,信度保费是在净保费原理下得到的,但在实际商业保险中,由于指数保费原理满足保费原理的所有性质,保险公司经常选择它来制定保费,在文献[27]中,温利民等人用均方损失函数得到了指数保费原理的信度估计.本文在平衡损失函数下建立了指数保费原理的信度估计,推广了温利民等人的结论. 其次,在实际应用中,随着每年物价变化,通货膨胀对于索赔额的影响予以考虑.本文在平衡损失函数下研究了具有通货膨胀因子的信度保费,得到了单合同模型和多合同模型对应的信度保费,并对结果进行了数值模拟,它符合预期结果. 最后,经典信度理论假设各风险之间互相独立,但在实际应用中,由于各风险之间并不是独立的,而是具有相依性的,在文献[28]中,温利民等人给出了个体索赔额间具有时间变化效应的特殊相关结构的信度保费.本文在平衡损失函数下研究了各风险间具有此种特殊相依结构的信度模型,分别得到了Buühlmann和Buühlmann-Straub模型的信度保费,结果表明它是经典信度模型 Buühlmann和Buühlmann-Straub模型的推广.
[Abstract]:The equilibrium loss function not only reflects the accuracy of the estimation, but also reflects the degree of fit. It has become a research topic in many fields, so the reliability theory is further studied in this paper under the equilibrium loss function. First of all, in the classical reliability theory, the reliability premium is obtained under the net premium principle, but in the actual commercial insurance, because the exponential premium principle satisfies all the properties of the premium principle, the insurance company often chooses it to make the premium. In reference [27], Wen Limin et al obtained the reliability estimation of the exponential premium principle by using the mean square loss function. In this paper, the reliability estimate of the exponential premium principle is established under the equilibrium loss function, which generalizes the conclusion of Wen Limin et al. Secondly, the effect of inflation on the amount claimed is considered with the change of annual price in practice. In this paper, the reliability premium with inflation factor is studied under the equilibrium loss function. The reliability premium corresponding to the single contract model and the multiple contract model is obtained, and the numerical simulation of the results is carried out, which is in accordance with the expected results. Finally, the classical reliability theory assumes that the risks are independent of each other, but in practice, because the risks are not independent, but are dependent, in the literature [28], Wen Limin et al gave the reliability premium of a special correlation structure with time-varying effect among individual claims. In this paper, the reliability model with such a special dependent structure between risks is studied under the equilibrium loss function. The reliability premiums of the Bu 眉 hlmann and Bu 眉 hlmann-Straub models are obtained, respectively, and the results show that they are generalizations of the classical reliability models Bu 眉 hlmann and Bu 眉 hlmann-Straub models.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F840.3

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