A well-designed framework for risk classification and ratemaking in automobile insurance is key to insurers' profitability and risk management, while also ensuring that policyholders are charged a fair premium according to their risk profile. In this paper, we propose to adapt a flexible regression model, called the Mixed LRMoE, to the problem of a posteriori risk classification and ratemaking, where policyholder-level random effects are incorporated to better infer their risk profile reflected by the claim history. We also develop a stochastic variational Expectation-Conditional-Maximization algorithm for estimating model parameters and inferring the posterior distribution of random effects, which is numerically efficient and scalable to large insurance portfolios. We then apply the Mixed LRMoE model to a real, multiyear automobile insurance dataset, where the proposed framework is shown to offer better fit to data and produce posterior premium which accurately reflects policyholders' claim history.
翻译:精心设计的汽车保险风险分类和评级框架是保险公司赢利和风险管理的关键,同时也确保投保人根据其风险简介收取公平溢价。在本文件中,我们提议对一个称为 " 混合LRMoE " 的灵活回归模型进行调整,以适应后生风险分类和评级问题,在后生风险分类和评级问题上,纳入投保人一级的随机效应,以更好地推断索赔历史所反映的风险简介。我们还开发了一种随机变化式预期-条件-最大化算法,用于估算模型参数,并推断随机效应的后生分布,这种效应在数字上是有效的,可扩缩到大型保险组合。 然后,我们将混合LRMOE模型应用于一个真实的、多年期汽车保险数据集,其中显示拟议框架更适合数据,并产生准确反映投保人索赔史的后生溢价。