Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning
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机器学习保险定价中的自校准与Tweedie优势关系
- 研究问题
- 保险定价模型最小化Tweedie偏差时为何可能失去预测与观测的平衡，如何校正局部偏差并比较竞争模型？
- 方法与思路
- 作者分析Tweedie偏差最小化中部分矩差异与特定尺度偏差的权衡，增加局部GLM步骤实施自校准，并讨论凸序比较。
- 材料陈述的贡献
- 摘要称自校准将纯保费预测的平衡从组合总体推进到局部尺度，并提出用凸序理解模型比较、诊断图与评价指标。
- 阅读关注点
- 应核对自校准的数学定义、局部GLM步骤和理论条件，以及局部平衡、凸序与Tweedie优势关系之间的联系。
- 阅读边界
- 这是arXiv预印本，同行评审与期刊接收未核实；摘要未说明校准条件和样本外表现，局部平衡不直接保证预测更准。
原文摘要
Boosting techniques and neural networks are particularly effective machine learning methods for insurance pricing. Often in practice, there are nevertheless endless debates about the choice of the right loss function to be used to train the machine learning model, as well as about the appropriate metric to assess the performances of competing models. Also, the sum of fitted values can depart from the observed totals to a large extent and this often confuses actuarial analysts. The lack of balance inherent to training models by minimizing deviance outside the familiar GLM with canonical link setting has been empirically documented in Wüthrich (2019, 2020) who attributes it to the early stopping rule in gradient descent methods for model fitting. The present paper aims to further study this phenomenon when learning proceeds by minimizing Tweedie deviance. It is shown that minimizing deviance involves a trade-off between the integral of weighted differences of lower partial moments and the bias measured on a specific scale. Autocalibration is then proposed as a remedy. This new method to correct for bias adds an extra local GLM step to the analysis. Theoretically, it is shown that it implements the autocalibration concept in pure premium calculation and ensures that balance also holds on a local scale, not only at portfolio level as with existing bias-correction techniques. The convex order appears to be the natural tool to compare competing models, putting a new light on the diagnostic graphs and associated metrics proposed by Denuit et al. (2019).