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由于巨灾损失通常存在极端值,一般的统计分布很难对其进行有效拟合。本文以我国大陆地区1950—2015年期间的地震灾害为研究样本,基于二维泊松过程建立了地震灾害死亡人数的预测模型。根据地震死亡人数的分布特征,将地震灾害分为非巨灾事件和巨灾事件,分别用右截断负二项分布和右截断广义帕累托分布拟合死亡人数;用齐次泊松过程描述地震灾害在给定期间的发生次数;用Panjer迭代法和快速傅里叶变换计算地震死亡人数在特定时期的分布以及风险度量值;用蒙特卡罗模拟法测算我国地震死亡保险基金的规模和纯保费水平。与传统的巨灾模型相比,本文提出的方法同时考虑了地震灾害发生的时间和地震死亡人数两个维度,并用贝叶斯方法估计模型参数,对地震死亡人数的拟合更加合理,为完善我国地震死亡保险提供了一种新的思路。
Abstract：Catastrophe insurance system depends on modeling of catastrophe loss data. The general statistical distributions are not suitable for fitting the catastrophic loss data since it usually contains some extreme values. This paper collected the loss data of earthquakes during the years 1950—2015 in China and modeled the earthquake deaths using the two dimensional Poisson process. First,we separated the earthquakes into two types according to the dearth numbers,the dearth numbers of the first type is been fitted by the righttruncated negative binominal distribution and the dearth numbers of the second type is fitted by the righttruncated generalized Pareto distribution. The two dimensional Poisson process is applied to model the occurrences of earthquakes. Panjer iterative method and fast Fourier transform method are been used to calculate the distribution of the earthquake deaths during a certain period. Finally,MCMC method is been applied to calculate the earthquake death insurance fund. The method proposed in the paper makes use of the earthquake time and earthquake deaths,and Bayesian technique is been used to estimate the parameters of the model,so it leads to a more accurate result than traditional methods. The method in the paper provides a new way for improving earthquake death insurance in China.
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基本信息:
DOI：10.19343/j.cnki.11-1302/c.2018.10.008
中图分类号:F842.64;D632.5
引用信息:
[1]孟生旺,李政宵.地震死亡人数预测与巨灾保险基金测算[J].统计研究,2018,35(10):89-102.DOI:10.19343/j.cnki.11-1302/c.2018.10.008.
基金信息:
国家社会科学基金重大项目“巨灾保险的精算统计模型及其应用研究”(16ZDA052);; 教育部人文社会科学重点研究基地重大项目“基于大数据的精算统计模型与风险管理问题研究”(16JJD910001);; 对外经济贸易大学“风险依赖与精算费率厘定系统研究创新团队”(CXTD9-04)的资助
2018-10-25
2018-10-25