The prediction of future insurance claims based on observed risk factors, or covariates, help the actuary set insurance premiums. Typically, actuaries use parametric regression models to predict claims based on the covariate information. Such models assume the same functional form tying the response to the covariates for each data point. These models are not flexible enough and can fail to accurately capture at the individual level, the relationship between the covariates and the claims frequency and severity, which are often multimodal, highly skewed, and heavy-tailed. In this article, we explore the use of Bayesian nonparametric (BNP) regression models to predict claims frequency and severity based on covariates. In particular, we model claims frequency as a mixture of Poisson regression, and the logarithm of claims severity as a mixture of normal regression. We use the Dirichlet process (DP) and Pitman-Yor process (PY) as a prior for the mixing distribution over the regression parameters. Unlike parametric regression, such models allow each data point to have its individual parameters, making them highly flexible, resulting in improved prediction accuracy. We describe model fitting using MCMC and illustrate their applicability using French motor insurance claims data.

翻译：基于观测到的风险因素（协变量）预测未来保险理赔，有助于精算师设定保险费率。传统上，精算师使用参数回归模型根据协变量信息进行预测。这类模型假设每个数据点对应的响应变量与协变量之间具有相同的函数形式。这种模型灵活性不足，难以在个体层面准确捕捉协变量与理赔频率及严重性之间的关系，而后者往往呈现多峰、高度偏斜且具有厚尾特征。本文探索利用贝叶斯非参数（BNP）回归模型基于协变量预测理赔频率与严重性。具体而言，我们将理赔频率建模为泊松回归的混合，将理赔严重性的对数建模为正态回归的混合。回归参数上的混合分布采用狄利克雷过程（DP）和皮特曼-约尔过程（PY）作为先验。与参数回归不同，此类模型允许每个数据点拥有其个体参数，从而具有高度灵活性，可提升预测精度。我们描述了基于马尔可夫链蒙特卡洛（MCMC）的模型拟合方法，并利用法国机动车保险理赔数据展示了其适用性。