索赔准备金评估的非线性分层增长曲线模型研究

考虑损失流量三角形中同一事故年的损失随时间反复观测的纵向特征,将损失流量三角形视为分层数据,结合损失进展的增长曲线,提出了关于索赔准备金评估的两种非线性分层增长曲线模型,并应用R软件对精算实务中的实例给出了数值分析。提出的非线性分层模型为考虑多个事故年的损失进展建模提供了一种自然灵活的框架,使得建立的模型易于理解,同时在分层建模中纳入了增长曲线,也有效避免了尾部进展因子的选定问题。

Non-linear Hierarchical Growth Curve Models for Claims Reserving

The longitudinal characteristics of repeated measurements over time of loss for a given accident year in the loss runoff triangles has been considered in the paper. And the loss runoff triangles is regarded as hierarchical data. Then combined with the growth curves of loss development process, two non-linear hierarchical growth curve models of claims reserving are proposed in the paper, the first is called the hierarchical models based on loss development factors, and the second is called the hierarchical models based on Cape Cod assumption. Some numerical illustrations from actuarial practice are provided using R software. The proposed non-linear hierarchical growth curve models provide a natural and flexible framework to model loss development across multiple accident years. The method of non-linear growth curves together with hierarchical modeling techniques not only allows one to build models that are easy to understand, but also incorporates the growth curves into hierarchical modeling so as to effectively avoid the choices of tail development factors.