基于藤Copula的GAMLSS模型与非寿险准备金评估

Non-life Insurance Claims Reserving Based on Vine Copula and GAMLSS

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的GAMLSS模型,并将此模型应用于一组具有明显异方差的车险数据,拟合效果优于均值回归模型.另外,在多个业务线的准备金估计中,不同业务线之间的相依性通过藤Copula函数来描述.用D藤Copula描述相依关系的GAMLSS模型对准备金的评估结果既优于独立假设下的GAMLSS模型和链梯法对准备金的评估结果,同时还刻画了不同业务线之间的尾部相依性.

Under the assumption that the incremental paid claims of every line of business follow gamma distribution, inverse-Gaussian distribution and log-normal distribution,respectively,the corresponding GAMLSS models were established. The models were applied to a heteroscedastic data set of auto insurance claims,and the result shows that GAMLSS models are superior to mean regression models in predicting outstanding claim reserve.In practice,different lines of insurance business are,to some extent and their dependence can be captured by Vine Copula functions.The corresponding Vine Copula and GAMLSS models were established.The result shows that D Vine Copula-based GAMLSS model is superior to independent GAMLSS models and Chain Ladder method in claims reserving,and it also describes the tail dependence of different lines of business.