增量索赔准备金的高斯过程回归模型
Gaussian Process Regression Model for Incremental Claim Reserves
摘要: 在保险实践中，索赔管理、业务实践、货币政策和立法变化经常发生，这将会对在同一日历年发生的索赔产生相同影响。对来自同一日历年的多个索赔之间的相关关系进行建模有可能进一步提高预测精度。本文尝试利用高斯过程回归(GPR)和复合核方法对经过对数转换后的增量索赔数据进行建模，从而引入同一日历年间的相关关系，提升预测精度。我们对来自NAIC数据库的三条业务线进行了实证分析，比较并展示了我们模型的性能，为今后的研究提供了新的思路。
Abstract: In insurance practice, claims management, business practices, monetary policy and legislative changes occur frequently, which will have the same impact on claims occurring in the same calen-dar year. Modelling correlations between multiple claims from the same calendar year has the po-tential to further improve forecasting accuracy. In this paper, Gaussian process regression (GPR) and composite kernel method are used to model the log-transformed incremental claim data, so as to introduce the correlation between the same calendar year and improve the prediction accuracy. We conducted empirical analysis on three lines of business from NAIC database, compared and demonstrated the performance of our models, which provided a new idea for future research.
文章引用：邓旭生, 卢志义. 增量索赔准备金的高斯过程回归模型[J]. 应用数学进展, 2023, 12(3): 1299-1305. https://doi.org/10.12677/AAM.2023.123132

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