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在保险实践中，损失数据的厚尾性会导致均值回归的结果不合理。为此，本文将分位回归与梯度提升树相结合，提出分位回归提升树模型，用树结构来描述风险因子与响应变量分位数之间的复杂关系。出于单调性的考虑，利用加法结构和乘法结构将分位回归提升树推广到多水平形式，同时预测多个水平下的分位数，并将多任务学习中的硬参数共享思想引入多水平模型，从而减少参数个数，降低模型复杂度。本文提出的方法在模拟数据和真实数据上都表现出良好的预测性能和可解释性，为保险定价和风险管理提供一种新的数据分析工具和方法。
Abstract：In insurance practice, the heavy tailed nature of loss data can lead to unreasonable results in mean regression. Therefore, combining quantile regression and gradient boosting tree, this paper proposes a quantile regression boosting tree model, which uses a tree structure to describe the complex relationship between risk factors and the quantiles of response variables. Considering the monotonicity, the additive structure and multiplicative structure are used to extend the quantile regression boosting tree to multiple forms, enabling it to synchronously predict quantiles at multiple levels. Next, the idea of hard parameter sharing in multi-task learning is introduced into the multivariate model to reduce the number of parameters and model complexity. The method proposed in this paper exhibits good predictive performance and interpretability on both simulated data and real data, providing a new data analysis tool and method for insurance ratemaking and risk management.
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(1)因篇幅所限，分位回归模型在驾驶行为数据上的样本外损失和CR值以附表1展示，见《统计研究》网站所列附件。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2026.01.009
中图分类号:F842;O212.1
引用信息:
[1]高雅倩,黄一凡,孟生旺.多水平分位回归提升树模型与保险损失预测[J].统计研究,2026,43(01):122-135.DOI:10.19343/j.cnki.11-1302/c.2026.01.009.
基金信息:
国家社会科学基金重点项目“巨灾债券定价与风险管理的统计建模研究”（22ATJ005）; 国家自然科学基金青年项目“基于多任务机器学习的非寿险相依风险模型研究”（72201062）
2025-04-23
2025
2026-01-05
2026-01-27
2026
1
2026-01-25
2026-01-25