为了助力传统产业转型升级，探索统计理论与应用融合发展，基地重大项目“数字时代风险管理与精算模型研究”应用大数据和人工智能方法对风险管理与保险精算领域的若干重要问题进行了研究，包括宏观经济金融风险管理、农业风险管理、保险产品与服务等领域。以下是项目组在车险定价和非寿险准备金评估领域中的一些近期研究成果。

1.Gao G. Fitting Tweedie's compound Poisson model to pure premium with the EM algorithm[J]. Insurance: Mathematics and Economics, 2024, 114: 29-42.

2.高雅倩,孟生旺.双参数Tweedie机器学习模型及其精算应用[J].统计研究,2024,41(04):126-140.

3.Chang L, Gao G, Shi Y. A semi-parametric claims reserving model with monotone splines[J]. Annals of Operations Research, 2024: 1-37. Online

4.Chang L, Gao G, Shi Y. Claims reserving with a robust generalized additive model[J]. North American Actuarial Journal, 2024: 1-21. Online

论文题目与摘要

1.Gao G. Fitting Tweedie's compound Poisson model to pure premium with the EM algorithm[J]. Insurance: Mathematics and Economics, 2024, 114: 29-42.

Abstract: We consider the situation when the number of claims is unavailable, and a Tweedie's compound Poisson model is fitted to the observed pure premium. Currently, there are two different models based on the Tweedie distribution: a single generalized linear model (GLM) for mean and a double generalized linear model (DGLM) for both mean and dispersion. Although the DGLM approach facilitates the heterogeneous dispersion, its soundness relies on the accuracy of the saddlepoint approximation, which is poor when the proportion of zero claims is large. For both models, the power variance parameter is estimated by considering the profile likelihood, which is computationally expensive. We propose a new approach to fit the Tweedie model with the EM algorithm, which is equivalent to an iteratively re-weighted Poisson-gamma model on an augmented data set. The proposed approach addresses the heterogeneous dispersion without needing the saddlepoint approximation, and the power variance parameter is estimated during the model fitting. Numerical examples show that our proposed approach is superior to the two competing models.

Keywords: Tweedie’s compound Poisson model；Tweedie distribution；Exponential dispersion family；The EM algorithm；Generalized linear model

2. 高雅倩,孟生旺.双参数Tweedie机器学习模型及其精算应用[J].统计研究,2024,41(04):126-140.

摘要：Tweedie回归是保险损失预测和风险定价的主要工具之一。为充分利用大数据、物联 网、机器学习等技术促进保险业的数字化转型，实现更加精准的风险识别和风险定价，本文将传统的Tweedie广义线性模型推广到双参数形式，并结合机器学习算法，提出双参数Tweedie梯度提升树模 型和双参数Tweedie组合神经网络模型。基于我国一家保险公司的车联网大数据，提取了新的驾驶行 为风险因子。通过实证研究检验了双参数Tweedie梯度提升树和双参数Tweedie组合神经网络在风险识 别以及风险定价中的有效性，为促进我国保险业数字化转型提供了一种新的模型和方法。

关键词：Tweedie回归；双参数梯度提升树；双参数组合神经网络；驾驶行为因子

3. Chang L, Gao G, Shi Y. A semi-parametric claims reserving model with monotone splines[J]. Annals of Operations Research, 2024: 1-37. Online

Abstract: Stochastic reserving models used in the insurance industry are usually based on an assumed distribution of claim amounts. Despite their popularity, such models may unavoidably be affected by the misspecification issue given that it is likely that the underlying distribution will be different from that assumed. In this paper, we incorporate monotone splines to ensure the expected monotonically increasing pattern of cumulative development factors (CDFs) to develop a new semi-parametric reserving model that does not require a density assumption. To allow the maximum utilization of available information, we also propose an enhanced sampling approach that greatly increases the size of unbiased CDFs, particularly in later development periods. Based on the enhanced samples, a bootstrap technique is employed in the estimation of monotone splines, from which incurred-but-not-reported (IBNR) reserves and prediction errors can be obtained. Associated technical features, such as the consistency of estimator, are discussed and demonstrated. Our simulation studies suggest that the new model improves the accuracy of IBNR reserving, compared with a range of classic competing models. A real data analysis produces many consistent findings, thus supporting the usefulness of the monotone spline model in actuarial and insurance practice.

Keywords: Claims reserving; Chain-ladder technique; Monotone splines; Bootstrap

4. Chang L, Gao G, Shi Y. Claims reserving with a robust generalized additive model[J]. North American Actuarial Journal, 2024: 1-21. Online

Abstract: In the actuarial literature, many existing stochastic claims-reserving methods ignore the excessive effects of outliers. In practice, however, these outlying observations may occur in the upper triangle and can have a nontrivial and undesirable influence on the existing reserving models. In this article, we consider the situation when outliers of claims are present in the upper triangle. We demonstrate that the model fitting and prediction results of the classical chain-ladder method can be substantially affected by these outliers. To mitigate this negative effect, we propose a robust generalized additive model (GAM). An associated robust bootstrap based on stratified sampling is also developed to obtain a more reliable predictive bootstrap distribution of outstanding claims. Using both simulation examples and real data, we compare our proposed robust GAM with nonrobust counterparts and robust GLM. We demonstrate that the robust GAM provides comparable results with those of other models when outliers are not present and that the robust GAM demonstrates significant improvements in estimation accuracy and efficiency when outliers are present.

Keywords: Claims reserving; Chain-ladder technique; Generalized additive model