基于贝叶斯加性回归树的风险保费建模方法研究

Research on Risk Premium Modeling Methods Based on Bayesian Additive Regression Trees

摘要: 车险索赔数据普遍存在索赔发生不均衡、索赔金额重尾分布及风险特征高度非线性等问题，给风险保费建模带来挑战。本文提出一种融合机器学习与期望分位数(Expectile)保费原理的风险保费建模框架。该框架由“两阶段纯保费模型”和“贝叶斯期望分位数加性回归树(BEART)风险附加模型”两部分构成，分别用于刻画车险的出险概率和条件累计索赔额情况及索赔分布的尾部风险特征。实证结果表明，该框架在风险识别、尾部风险刻画及预测稳定性方面具有良好表现，可为复杂车险风险环境下风险保费厘定提供可靠的建模依据。

Abstract: Auto insurance claims data are commonly characterized by imbalanced claim occurrence, heavy-tailed claim severity distributions, and highly nonlinear risk features, posing substantial challenges for risk premium modeling. This paper proposes a risk premium modeling framework that integrates machine learning techniques with the Expectile premium principle. The framework consists of two components: a two-stage pure premium model and a Bayesian Expectile Additive Regression Tree (BEART)-based risk loading model, which are employed to characterize claim occurrence probability, conditional cumulative claim amounts, and tail risk features of the claims distribution, respectively. Empirical results demonstrate that the proposed framework exhibits strong performance in risk discrimination, tail risk characterization, and predictive stability, providing a reliable modeling basis for risk premium determination in complex motor insurance risk environments.