The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, macro-level catastrophic risk forecasting, as well as operational risk in banking regulation. This model, which is initially designed for cross-sectional data, has recently been adapted to a longitudinal context to conduct both a priori and a posteriori ratemaking, through the introduction of random effects. However, so far, the random effect(s) is usually assumed static due to computational concerns, leading to predictive premium that omit the seniority of the claims. In this paper, we propose a new CRM model with bivariate dynamic random effect process. The model is based on Bayesian state-space models. It is associated with the simple predictive mean and closed form expression for the likelihood function, while also allowing for the dependence between the frequency and severity components. Real data application to auto insurance is proposed to show the performance of our method.
翻译:频率和严重程度的集体风险模型(CRM)是零售保险率、宏观级灾难性风险预测以及银行监管业务风险的重要工具。该模型最初是为跨部门数据设计的,最近通过随机效应的引入,适应了纵向环境,进行先验和后验的评级。然而,迄今为止,随机效应通常由于计算考虑而假定为静态,从而导致预测溢价,忽略索赔的年资。在本文件中,我们提出了一个新的CRM模型,采用双变量动态随机效应程序。该模型以巴伊西亚州-空间模型为基础。该模型与概率函数的简单预测平均值和封闭形式表达相联,同时允许频率和严重程度组成部分之间的依赖性。提议对自动保险的实际数据应用以显示我们方法的性能。