基于中国数据的随机死亡率模型比较研究
发布时间：2019-02-16 15:38
【摘要】：传统的精算实务中,精算师运用生命表计算寿险产品定价。这种做法是建立在死亡率静态不变的假设之上的。然而,根据世界各国的历史人口统计数据,死亡率却是随时间而变动的,具有随机特征。近20年来,各种能够刻画死亡率随机特征的随机死亡率模型被开发了出来。如何根据我国的实际情况挑选合适的随机死亡率模型,从而更好地处理以及预测死亡率随着时间的变动,对政府社保系统、保险公司的寿险产品、企业的养老金以及目前国际上正在大力推进的长寿衍生品的设计与定价研究来说都是至关重要的。 本文挑选了经典Lee-Carter模型、Renshaw-Haberman模型、Currie模型、CBD模型及其三种扩展形、以及适用于老年人口的一种Plat模型特例,共八个具有代表性的随机死亡率模型,进行了模型结构、拟合以及外推方法的详细介绍,并针对我国1995-2011年17年间60-89岁男性老年人口的死亡情况进行了一系列定性与定量的比较研究。对于本文所使用的数据集的适用性所做的比较研究涉及三大方面：1.)与模型结构有关的性质：包括非负死亡率、易用性、简洁性、是否考虑出生年因素、不同年龄死亡率序列是否完全相关等。2.)与模型拟合相关的比较：包括BIC、似然比检验等极大似然值与惩罚项的比较,基于标准死亡残差服从独立标准正态分布假设的各种检验,以及参数鲁棒性比较。3.)与模型预测相关的比较：包括长期预测合理性,预测鲁棒性,及样本外预测精度。 比较后发现参数最少的经典CBD模型是最适用于我国男性老年数据集的,它是唯一一个在所有比较项目下均表现良好的模型。最后,本文根据我国老年男性数据集的特征以及对各模型比较中的一些发现,尝试引入了一种新的模型,将其与CBD模型进行比较,发现CBD模型仍然更胜一筹。
[Abstract]:In traditional actuarial practice, actuaries use life tables to price life insurance products. This approach is based on the assumption that mortality is static and constant. However, according to the world's historical demographic data, the mortality rate varies with time and has random characteristics. In recent 20 years, various random mortality models which can describe the random characteristics of mortality have been developed. How to select the appropriate random mortality model according to the actual situation in our country, so as to better deal with and predict the mortality rate over time, to the government social security system, to the life insurance products of insurance companies, Corporate pensions, as well as research into the design and pricing of longevity derivatives that are now being vigorously promoted internationally, are crucial. This paper selects the classical Lee-Carter model, Renshaw-Haberman model, Currie model, CBD model and its three extended forms, and a special case of Plat model for the elderly population. Eight representative random mortality models are selected and constructed. The fitting and extrapolation methods are introduced in detail, and a series of qualitative and quantitative comparative studies on the death of the aged male population aged 60-89 years from 1995 to 2011 in China are carried out. The comparative study of the applicability of the data set used in this paper involves three aspects: 1. Properties related to the structure of the model: including non-negative mortality, ease of use, brevity, whether birth factors are taken into account, whether different age mortality sequences are completely relevant, etc. Comparison with model fitting: the comparison of maximum likelihood value and penalty term such as BIC, likelihood ratio test, various tests based on standard death residuals hypothesis of independent standard normal distribution, and comparison of parameter robustness. Comparison with model prediction: long-term prediction rationality, prediction robustness, and prediction accuracy outside the sample. It is found that the classical CBD model with the least parameters is the most suitable for the male data set in China, and it is the only one that performs well under all comparative items. Finally, according to the characteristics of Chinese old male data sets and some findings in the comparison of each model, we try to introduce a new model and compare it with the CBD model. It is found that the CBD model is still superior.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：C924.24;F842.62
本文编号：2424586
[Abstract]:In traditional actuarial practice, actuaries use life tables to price life insurance products. This approach is based on the assumption that mortality is static and constant. However, according to the world's historical demographic data, the mortality rate varies with time and has random characteristics. In recent 20 years, various random mortality models which can describe the random characteristics of mortality have been developed. How to select the appropriate random mortality model according to the actual situation in our country, so as to better deal with and predict the mortality rate over time, to the government social security system, to the life insurance products of insurance companies, Corporate pensions, as well as research into the design and pricing of longevity derivatives that are now being vigorously promoted internationally, are crucial. This paper selects the classical Lee-Carter model, Renshaw-Haberman model, Currie model, CBD model and its three extended forms, and a special case of Plat model for the elderly population. Eight representative random mortality models are selected and constructed. The fitting and extrapolation methods are introduced in detail, and a series of qualitative and quantitative comparative studies on the death of the aged male population aged 60-89 years from 1995 to 2011 in China are carried out. The comparative study of the applicability of the data set used in this paper involves three aspects: 1. Properties related to the structure of the model: including non-negative mortality, ease of use, brevity, whether birth factors are taken into account, whether different age mortality sequences are completely relevant, etc. Comparison with model fitting: the comparison of maximum likelihood value and penalty term such as BIC, likelihood ratio test, various tests based on standard death residuals hypothesis of independent standard normal distribution, and comparison of parameter robustness. Comparison with model prediction: long-term prediction rationality, prediction robustness, and prediction accuracy outside the sample. It is found that the classical CBD model with the least parameters is the most suitable for the male data set in China, and it is the only one that performs well under all comparative items. Finally, according to the characteristics of Chinese old male data sets and some findings in the comparison of each model, we try to introduce a new model and compare it with the CBD model. It is found that the CBD model is still superior.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：C924.24;F842.62
【参考文献】
相关期刊论文 前2条
1 韩猛;王晓军;;Lee-Carter模型在中国城市人口死亡率预测中的应用与改进[J];保险研究;2010年10期
2 王晓军;黄顺林;;中国人口死亡率随机预测模型的比较与选择[J];人口与经济;2011年01期
，本文编号：2424586
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