《保险研究》20230308-《基于大样本模拟的巨灾损失计算方法》（高曹珀、王自法、周阳、WANG Jianming）

［摘   要］巨灾损失计算的精度影响着保险费率厘定、灾后补偿和防灾减灾工作的效果。传统的巨灾损失量化主要依赖均值和方差来表示损失的精度和不确定性,在复杂的叠加计算中需要增加各类相关性的假定,计算流程繁琐且精度不高。本研究引入克罗内克积表示各类耦合,基于高斯耦合和大样本模拟方法将复杂的概率分布转化为大样本集,较好地解决了各类耦合问题并且将时间域、空间域和损失不确定性等多个分布转化为样本集,从而简化了巨灾损失风险的计算。本文提出的方法不仅适用于地震巨灾,类似思路同样可以应用于台风、洪水等巨灾的损失计算,并以此简明地计算出对应各个风险水平的损失指标。最后本文以阿克苏地区拜城县的震害损失为例,进行示范性应用研究,给出了该地区的保险纯费率分布,验证了模型的有效性,并在此基础上,计算出直接经济损失及保险再保险损失的超越概率曲线,为未来城市的巨灾风险定价提供量化依据。

［关键词］大样本模拟方法；巨灾损失；巨灾风险；地震危险性；保险损失

［基金项目］本研究受到中国地震局工程力学研究所基本科研业务费专项资助项目（编号:2021B09）、国家自然科学基金面上项目（51978634）的大力支持。

［作者简介］高曹珀，河南大学土木建筑学院硕士研究生；王自法，中国地震局工程力学研究所研究员、中震科建（广东）防灾减灾研究院院长；周阳、WANG Jianming，就职于中震科建（广东）防灾减灾研究院。

The Calculation Method for Catastrophe Losses Based on Large-scale Sampling

GAO Cao-po,WANG Zi-fa,ZHOU Yang,WANG Jian-ming

Abstract：Earthquake catastrophe loss quantification and its accuracy directly affect premium rating and the risk diversification effect of catastrophe insurance and disaster prevention results.Traditional catastrophe risk quantification is often based on an estimate of a mean and its standard deviation to represent the estimation accuracy of loss and its uncertainty,but the calculation process is tedious and the accuracy is limited because of various assumptions made for correlation and coupling in the aggregation process.This study introduces the Kronecker product to represent the correlation and coupling and the Gaussian coupling and a large-scale simulation method to turn complicated probability distribution into large-scale samplings,solving the problem of various complex couplings,and transforming multiple distributions of time and space domains and loss uncertainty into sample sets.Thus simplifies the calculation of catastrophe loss risks.This method is not only suitable for earthquake catastrophe risk calculation,but also can be applied to the financial loss calculation of typhoon,flood and others,and concisely arriving at loss parameters corresponding to various levels of risks.Finally,using Baicheng County in Aksu region as an example,the earthquake loss is calculated and the net premium rate distribution is projected,verifying the validity of the model.In addition,exceeding probability (EP) curves for direct economic loss and reinsurance loss are calculated,providing quantitative references for catastrophe risk pricing of various cities in the future.

Key words：large-scale sampling;catastrophe losses;catastrophe risk;earthquake hazard;insurance losses