基于联合分位数回归的地震灾害二元损失评估模型及其应用

Bivariate Loss Assessment Model of Earthquake Disaster Based on Joint Quantile Regression and Its Application

地震灾害造成的直接损失包括经济损失和生命损失,两类损失数据特征存在较大差异,因此通常难以直接对其进行联合建模并量化二者在不同分位数水平下的相依性。鉴于此,笔者将非对称拉普拉斯分布与单变量分位数回归模型之间的联系扩展到二元背景,建立震级与死亡人数和直接经济损失的联合分位数回归模型。该模型无需针对两类损失分布予以假设,并且可以实现在险价值VaR和期望尾部损失ES的联合评估,从而为巨灾多元损失提供更加灵活准确与信息充分的量化框架。基于中国内地地区1990—2020年的地震灾害损失数据,利用EM算法估计系数,分别测算了二元损失在独立和相依情形下的VaR和ES,结果表明在相依性模型假设下,VaR和ES的估计结果会更加充足,故考虑二元损失的相依性是必要的。基于上述结果,笔者运用核估计方法进一步探讨了地震巨灾指数保险的制度设计与保费厘定问题。

The direct losses caused by earthquake disasters include economic losses and life losses.The characteristics of the two types of loss data are quite different,so it is difficult to quantify their dependence at different quantile levels directly.In view of this,we expand the relationship between the asymmetric Laplacian distribution and the univariate quantile regression model to the bivariate case,and establish the joint quantile regression model of magnitude,death toll and direct economic loss.The model does not need to make assumptions on the distribution of two types of loss,and can realize the joint evaluation of Value at Risk(VaR)and Expected Shortfall(ES),so as to provide a flexible,accurate and informative quantitative framework for bivariate catastrophe losses.Based on the data of earthquake disaster losses in China's Mainland from 1990 to 2020,the VaR and ES of bivariate losses are estimated using the EM algorithm in both independent and correlated cases.The results show that the estimation results of VaR and ES are more adequate under the assumption of dependency model,so it is necessary to consider the dependence between the bivariate losses.Based on the above results,kernel estimation is used to further explore the system design and premium determination of earthquake catastrophe index insurance.