The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, natural disaster forecasting, as well as operational risk in banking regulation. This model, initially designed for cross-sectional data, has recently been adapted to a longitudinal context for both a priori and a posteriori ratemaking, through random effects specifications. However, the random effects are usually assumed to be static due to computational concerns, leading to predictive premiums that omit the seniority of the claims. In this paper, we propose a new CRM model with bivariate dynamic random effects processes. The model is based on Bayesian state-space models. It is associated with a simple predictive mean and closed form expression for the likelihood function, while also allowing for the dependence between the frequency and severity components. A real data application for auto insurance is proposed to show the performance of our method.

频率和严重程度的集体风险模型 (CRM) 是零售保险费率制定、自然灾害预测以及银行监管中的操作风险的重要工具。这个模型最初是为横截面数据设计的，最近已经适应了先验和后验的纵向环境利率制定，通过随机效应规范。然而，由于计算问题，随机效应通常被假定为静态，导致预测保费忽略索赔的资历。在本文中，我们提出了一种具有双变量动态随机效应过程的新 CRM 模型。该模型基于贝叶斯状态空间模型。它与似然函数的简单预测均值和封闭形式表达式相关联，同时还允许频率和严重性分量之间的依赖性。提出了一个汽车保险的真实数据应用来展示我们方法的性能。