Traditional credibility analysis of risks in insurance is based on the random effects model, where the heterogeneity across the policyholders is assumed to be time-invariant. One popular extension is the dynamic random effects (or state-space) model. However, while the latter allows for time-varying heterogeneity, its application to the credibility analysis should be conducted with care due to the possibility of negative credibilities per period [see Pinquet (2020a)]. Another important but under-explored topic is the ordering of the credibility factors in a monotonous manner -- recent claims ought to have larger weights than the old ones. This paper shows that the ordering of the covariance structure of the random effects in the dynamic random effects model does not necessarily imply that of the credibility factors. Subsequently, we show that the state-space model, with AR(1)-type autocorrelation function, guarantees the ordering of the credibility factors. Simulation experiments and a case study with a real dataset are conducted to show the relevance in insurance applications.
翻译:保险风险的传统可信度分析以随机效应模型为基础,该模型假定所有投保人之间的差异是时间变化的。一个流行的扩展是动态随机效应(或国家空间)模型。然而,虽然后者允许时间变化的异质性,但在对可信度分析的应用中,应谨慎从事,因为每个时期都可能有负概率[见Pinquet (202020a)]。另一个重要但探索不足的主题是以单调方式排列可信度因素 -- -- 最近的索赔应当比旧索赔具有更大的权重。本文显示,动态随机效应模型随机效应的共变结构的排序并不一定意味着可信度因素。随后,我们表明,带有AR(1)型自动关系功能的状态空间模型保证了可靠性因素的排序。将进行模拟实验和进行一项案例研究,并用真实数据集来显示保险应用中的关联性。