用贝叶斯决策树建模保险索赔，更准预测总损失。
Bayesian CART models for aggregate claim modeling
- 构建三类贝叶斯决策树模型，融合索赔频次与金额
- 威布尔分布比伽马、对数正态更擅长捕捉尾部特征
- 联合建模优于独立假设，适合有依赖关系的保险数据
本文提出三种用于聚合索赔金额的贝叶斯决策树（BCART）模型：频次-严重性模型、序列模型和联合模型。针对多变量响应数据，提出通用框架，特别适用于双变量响应的联合模型（索赔次数与总索赔金额）。为支持频次-严重性建模，研究了多种分布对右偏重尾索赔严重性数据的拟合效果，发现威布尔分布因能灵活刻画树模型中的不同尾部特性，优于伽马和对数正态分布。此外，考虑到索赔次数与平均严重性间的相关性，序列型和联合型BCART模型表现更优，因此优于假设独立的频次-严重性模型。通过精心设计的模拟实验和真实保险数据验证了这些模型的有效性。
原文摘要 · Abstract (English)
This paper proposes three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We propose a general framework for the BCART models applicable to data with multivariate responses, which is particularly useful for the joint BCART models with a bivariate response: the number of claims and aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data by using various distributions. We discover that the Weibull distribution is superior to gamma and lognormal distributions, due to its ability to capture different tail characteristics in tree models. Additionally, we find that sequential BCART models and joint BCART models, which incorporate dependence between the number of claims and average severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is assumed. The effectiveness of these models' performance is illustrated by carefully designed simulations and real insurance data.
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