Automatic Segmentation of Insurance Rating Classes Under Ordinal Constraints via Group Fused Lasso

Atsumori Takahashi, S. Nomura
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Abstract

Abstract This paper proposes a sparse regularization technique for ratemaking under practical constraints. In tariff analysis of general insurance, rating factors with many categories are often grouped into a smaller number of classes to obtain reliable estimate of expected claim cost and make the tariff simple to reference. However, the number of rating-class segmentation combinations is often very large, making it computationally impossible to compare all the possible segmentations. In such cases, an L1 regularization method called the fused lasso is useful for integrating adjacent classes with similar risk levels in its inference process. Particularly, an extension of the fused lasso, known as the group fused lasso, enables consistent segmentation in estimating expected claim frequency and expected claim severity using generalized linear models. In this study, we enhance the group fused lasso by imposing ordinal constraints between the adjacent classes. Such constraints are often required in practice based on bonus–malus systems and actuarial insight on risk factors. We also propose an inference algorithm that uses the alternating direction method of multipliers. We apply the proposed method to motorcycle insurance claim data, and demonstrate how some adjacent categories are grouped into clusters with approximately homogeneous levels of expected claim frequency and severity.
基于群融合套索的有序约束下保险等级分类自动分割
提出了一种基于稀疏正则化的实际约束下的速率生成技术。在一般保险费率分析中,往往将多类别的费率因素归为少数几个类别,以获得可靠的预期索赔成本估计,并使费率易于参考。然而,分级分割组合的数量通常非常大,使得在计算上不可能比较所有可能的分割。在这种情况下,称为融合套索的L1正则化方法对于在其推理过程中集成具有相似风险水平的相邻类非常有用。特别是,融合套索的扩展,称为组融合套索,可以使用广义线性模型在估计预期索赔频率和预期索赔严重性方面进行一致的分割。在本研究中,我们通过在相邻类之间施加顺序约束来增强群体融合套索。在实践中,基于奖惩制度和对风险因素的精算洞察力,通常需要这样的约束。我们还提出了一种使用乘法器交替方向法的推理算法。我们将所提出的方法应用于摩托车保险索赔数据,并演示了如何将一些相邻类别分组到具有近似均匀的预期索赔频率和严重性水平的集群中。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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