相依风险的车险准备金评估

在多个业务线的准备金估计中,通常假设不同业务线之间相互独立,事实上它们之间往往存在一定的相依关系.它们的相依性可以通过藤Copula函数来描述.藤Copula是解决多个相依随机变量的强有力工具.本文在假设各个业务线的增量已决赔款服从伽玛分布、逆高斯分布和对数正态分布的基础上,建立了各个业务线增量已决赔款相互依赖的藤Copula回归模型,并将此模型应用于一组实际的车险数据,结果表明,考虑相依关系的藤Copula回归模型对准备金的评估结果要优于独立假设下的回归模型对准备金的评估结果.

Automobile insurance claims reserving for dependent risks

It is usually assumed that different lines of business are independent, but the fact is that they are dependent to some extent in multi-lines of business. Their dependence may be captured by Vine Copula functions. Vine Copula is a powerful tool to solve multiple dependence. Under the assumption that the incremental paid claims of every line of business follows gamma distribution, inverse-Gaussian distribution and log-normal distribution, respectively, the corresponding Vine Copula regression models are established. The model is applied to a real data set of auto insurance and the result shows that the Vine Copula-based regression model is superior to independent regression models in claims reserving.