基于Esscher损失函数和最大熵方法的的递推信度模型

发布时间：2018-04-13 19:38

本文选题：递推信度模型 + 最大熵　；参考：《新疆大学》2017年硕士论文

【摘要】：信度理论就是研究如何根据历史索赔额来解决保险费率的合理制定问题,在非寿险精算和保险实务中对下个时期的保费定价具有重要意义,主要是通过结合单个投保人的索赔经验数据与其他保单组合过去索赔经验数据来计算未来保费的一种定量方法,这种方法被广泛的应用于保险的各个领域,一般情况下,所得的保费为个体保费与集体保费的加权和.一方面,本文在递推信度模型的基础上,结合最大熵方法,得到了最大熵方法下的递推信度模型,考虑均方误差最小和熵最大原则,进行两次优化得到未来保费以及递推信度模型中信度因子的表达式,并且得到两种特殊的权重结构:一种是年份较近的索赔额有较大的权重另一种是年份较远的索赔额有较大的权重.另一方面,采用经典信度理论得到的信度保费均是纯保费原理下得到的,不具有保费的安全负荷,本文将在Esscher损失函数下,假设未来索赔具有推广后的递推形式,然后建立Esscher损失函数下的递推信度模型以及广义加权Esscher损失函数下的递推信度模型.最后,在实际中,保险合同之间的索赔具有某种相依性,本文将对相依结构的多合同信度模型作进一步的研究,包括齐次和非齐次的情况.
[Abstract]:The reliability theory is to study how to solve the problem of how to make the insurance rate reasonably according to the historical claim amount, which is of great significance to the premium pricing in the next period in the non-life insurance actuarial and insurance practice.It is a quantitative method to calculate the future premium mainly by combining the individual policyholder's claim experience data with other policies' combination of the past claim experience data. This method is widely used in various fields of insurance, generally speaking,The premium is the weighted sum of individual premium and collective premium.On the one hand, on the basis of the recursive reliability model and combined with the maximum entropy method, the recursive reliability model under the maximum entropy method is obtained, and the minimum mean square error and the maximum entropy principle are considered.Two optimizations are carried out to obtain the expressions of the future premium and the CITIC factor of the recursive reliability model.Two special weight structures are obtained: one is that the claim amount with a near year has a larger weight, and the other is that the claim amount with a longer year has a larger weight.On the other hand, the reliability premiums obtained by the classical reliability theory are all obtained under the pure premium principle and do not have the safety load of the premium. In this paper, under the Esscher loss function, we assume that the future claims have a generalized recursive form.Then the recursive reliability model under the Esscher loss function and the recursive reliability model under the generalized weighted Esscher loss function are established.Finally, in practice, the claims between insurance contracts have some dependence. In this paper, we will further study the multi-contract reliability model of dependent structures, including homogeneous and non-homogeneous cases.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840.4

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