地震损失风险的Copula混合分布模型及其应用  

Copula-mixed distribution model and its application in modeling earthquake loss in China

作　　者：刘新红[1] 孟生旺[2] 李政宵 LIU Xinhong;MENG Shengwang;LI Zhengxiao(Department of Mathematics and Physics,Beijing Institute of Petro-chemical Technology,Beijing 102617,China;Centerfor Applied Statistics,Renmin University of China,Beijing 100872,China;School of Insurance and Economics,University of International Business and Economics,Beijing 100029,China)

机构地区：[1]北京石油化工学院数理系,北京102617 [2]中国人民大学应用统计科学研究中心,北京100872 [3]对外经济贸易大学保险学院,北京100029

出　　处：《系统工程理论与实践》2019年第7期1855-1866,共12页Systems Engineering-Theory & Practice

基　　金：国家社科基金重大项目(16ZDA052);教育部人文社会科学重点研究基地重大项目(16JJD910001);中央高校建设世界一流大学(学科)专项资金~~

摘　　要：地震造成的损失主要包括直接经济损失和人员伤亡.本文以我国1950-2015年期间的地震灾害统计数据作为研究样本,建立了地震灾害造成的直接经济损失和死亡人数的Copula混合分布模型.在该模型中,用右截断的Gumble分布与广义帕累托分布构造的混合分布拟合对数直接经济损失,用两端截断的负二项分布与广义帕累托分布构造的混合分布拟合死亡人数,用Copula函数建立直接经济损失与死亡人数之间的相依关系,并通过蒙特卡罗模拟计算风险相依情况下地震灾害的风险度量值.与传统的地震灾害模型相比,本文提出的直接经济损失与死亡人数的Copula混合分布模型对巨灾数据的拟合更加合理,为我国建立地震巨灾保险制度提供了一种可供选择的精算模型.The direct economical losses and the tolls of earthquakes are main impacts of earthquake insurance.This paper collected the loss data of earthquake during the years 1950-2015 in China and modeled the direct economical losses and the tolls of earthquake using Copula-mixed distribution model.First,the truncated Gumble distribution and generalized Pareto distribution are mixed to fit the direct economical losses,and the truncated negative binominal distribution and generalized Pareto distribution are mixed to fit the tolls of earthquake.Second,copulas are used to model the dependence between the direct economical losses and the tolls of earthquake.Finally,Monte Carlo simulation method is used to calculate VaR and ES.The models proposed in the paper may be applied to establish earthquake insurance system in China.

关 键 词：地震风险 COPULA函数 广义帕累托分布 截断Gumble分布 截断负二项分布 

分 类 号：O212[理学—概率论与数理统计] F222.3[理学—数学]