平衡损失函数下的信度模型及其应用
发布时间：2018-07-29 16:24
【摘要】：传统的精算科学一般受限于人寿保险业。随后发展成为寿险精算。然而,由于信息技术的迅猛发展,特别到了二战以后。我们着手创立了风险理论。它使非寿险精算技术逐渐发展成熟,并形成了现在的非寿险精算科学。 非寿险精算的发展要比寿险精算晚得多。这是由于某些特殊原因的存在,使得非寿险精算问题具有更加复杂的定量分析方法。到目前为止,非寿险精算科学已发展成两个重要部分——风险理论和损失分布理论。 首先,本文在平方损失函数的基础上,依据贝叶斯决策以及信度理论,引入惩罚函数,通过加权方法,从而建立了具有非对称性的平衡损失函数。然后,根据新建立的损失函数。本文分别利用Buhlmann信度以及Buhlmann-Straub信度这两种方法。其信度保费估计式都为线性表达式,计算简单,并具有很强的实用性。再次,依据本文创设的Buhlmann信度模型,分别利用非参数估计方法、泊松半参数估计方法以及Normal-Normal参数估计方法,对信度因子以及索赔频率进行可信性估计,并进行了实证分析研究。
[Abstract]:Traditional actuarial science is generally limited to the life insurance industry. Subsequently developed into life insurance actuarial. However, due to the rapid development of information technology, especially after World War II. We set out to create the theory of risk. It makes the non-life actuarial technology develop and mature gradually, and forms the non-life actuarial science. The development of non-life actuarial insurance is much later than that of life insurance actuarial. Because of the existence of some special reasons, the non-life insurance actuarial problem has more complicated quantitative analysis method. Up to now, non-life actuarial science has developed into two important parts: risk theory and loss distribution theory. Firstly, on the basis of square loss function, according to Bayesian decision and reliability theory, the penalty function is introduced, and the balance loss function with asymmetry is established by weighted method. Then, according to the newly established loss function. In this paper, Buhlmann reliability and Buhlmann-Straub reliability are used respectively. The reliability premium estimators are linear expressions, which are simple to calculate and have strong practicability. Thirdly, according to the Buhlmann reliability model created in this paper, the reliability factor and claim frequency are estimated by using non-parametric estimation method, Poisson semi-parameter estimation method and Normal-Normal parameter estimation method, and the empirical analysis is carried out.
【学位授予单位】：北京化工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840.4;F224
本文编号：2153272
[Abstract]:Traditional actuarial science is generally limited to the life insurance industry. Subsequently developed into life insurance actuarial. However, due to the rapid development of information technology, especially after World War II. We set out to create the theory of risk. It makes the non-life actuarial technology develop and mature gradually, and forms the non-life actuarial science. The development of non-life actuarial insurance is much later than that of life insurance actuarial. Because of the existence of some special reasons, the non-life insurance actuarial problem has more complicated quantitative analysis method. Up to now, non-life actuarial science has developed into two important parts: risk theory and loss distribution theory. Firstly, on the basis of square loss function, according to Bayesian decision and reliability theory, the penalty function is introduced, and the balance loss function with asymmetry is established by weighted method. Then, according to the newly established loss function. In this paper, Buhlmann reliability and Buhlmann-Straub reliability are used respectively. The reliability premium estimators are linear expressions, which are simple to calculate and have strong practicability. Thirdly, according to the Buhlmann reliability model created in this paper, the reliability factor and claim frequency are estimated by using non-parametric estimation method, Poisson semi-parameter estimation method and Normal-Normal parameter estimation method, and the empirical analysis is carried out.
【学位授予单位】：北京化工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840.4;F224
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