地震损失风险的Copula混合分布模型及其应用

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.

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

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.