基于Mixed Erlang-Pareto组合分布的巨灾风险评估——以中国地震灾害为例  

Catastrophe Risk Assessment Based on Mixed Erlang-Pareto Combination Distribution Model:A Case of Earthquake Disaster in China

作　　者：郭静 张连增 GUO Jing;ZHANG Lian-zeng(School of Finance,Nankai University,Tianjin 300350,China)

机构地区：[1]南开大学金融学院,天津300350

出　　处：《统计与信息论坛》2021年第3期119-128,共10页Journal of Statistics and Information

基　　金：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);天津市哲学社会科学规划项目“天津市城市公共安全与突发重大环境灾害风险评价与保险制度创新设计”(TJYY16-005)。

摘　　要：巨灾损失数据具有尖峰厚尾的特征,通常的损失分布模型很难对其进行有效地拟合。针对常见的各类分布(如Gamma,Lognormal,Weibull)和POT-GPD损失分布对巨灾风险损失数据拟合的不足,将截断形式的Mixed Erlang分布与Pareto分布进行组合,构建组合分布模型,充分应用了Mixed Erlang分布对阈值之前损失数据拟合分布形式的灵活性和精确性,以及Pareto分布对阈值之后尾部损失数据拟合的优良性,从而与以往方法相比,能够从整体上更精确地拟合巨灾风险损失数据。在此基础上,对中国1990—2018年4.5级以上地震所造成的直接经济损失数据进行组合分布建模,探讨该组合分布在VaR、TVaR和地震巨灾保险定价等方面的具体应用。研究发现:构建的Mixed Erlang-Pareto组合分布可以较好地拟合地震巨灾风险损失数据,且拟合优度高于Mixed Erlang-GDP组合分布;在忽略其他因素影响下,假定参保率为30%时,应用Mixed Erlang-Pareto分布计算的地震巨灾保险人均纯保费为40~43元左右,和四川省宜宾市城乡居民住宅地震巨灾保险保费相近,说明该地震巨灾保险保费的确定存在一定合理性。此外,对Mixed Erlang-Pareto组合分布拟合优度进一步检验,得出该组合分布也可以较好地拟合洪水损失数据,进一步表明该组合分布对巨灾损失数据拟合的优良性和适用性。本研究可以为巨灾损失风险评估提供一种新的备选模型,也可以作为评估巨灾保险定价机制合理与否的精算依据。The catastrophe loss data has the characteristics of sharp peaks and thick tails,and it is difficult to effectively fit the normal loss distribution model.In view of the inadequacies of common distributions(such as Gamma,Lognormal,Weibull)and POT-GPD loss distributions on catastrophe risk loss data.Combining the truncated Mixed Erlang distribution with Pareto distribution to build a combined distribution,which can fully utilize the flexibility and accuracy of the Mixed Erlang distribution on the loss data,and the optimal fitting of the Pareto distribution on the tail data is larger than the threshold,which can fit catastrophe risk loss data more accurately as a whole compared with the previous methods.On the basis,conducting a combined distribution modeling with the direct economic loss data caused by the earthquakes of magnitude 4.5 and above in China's Mainland from 1990 to 2018.discussing some applications of the combined distribution as regards VaR,TVaR and earthquake catastrophe insurance pricing.It is found that the constructed Mixed Erlang-Pareto combined distribution can better fit the earthquake catastrophe risk loss data,and the goodness of fit is higher than the Mixed Erlang-GDP combined distribution.Ignoring the influence of other factors,assuming that the participation rate is 30%,per capita net insurance premium for earthquake catastrophe calculated by Mixed Erlang-Pareto distribution is between 40 and 43 yuan,which is similar to the earthquake catastrophe insurance premium for urban and rural residents in Yibin,Sichuan Province.The formulation of the earthquake catastrophe insurance premium is reasonable.In addition,the goodness of the fit of the Mixed Erlang-Pareto combination distribution is further tested,and it is concluded that the combined distribution can also fit the flood loss data well,which further shows the superior and applicable to the fitting of catastrophe data.Here a new alternative model is provided for earthquake catastrophe loss risk assessment,which can also be used as an actua

关 键 词：巨灾风险 Mixed Erlang-Pareto组合 在险价值 尾部在险价值 巨灾保险定价 

分 类 号：F840.64[经济管理—保险]