Lande Chrisandi R, Iriawan Nur, Prastyo Dedy Dwi
Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111 Indonesia.
Politeknik Ilmu Pelayaran Makassar, Makassar 90165, Indonesia.
MethodsX. 2024 Dec 9;14:103095. doi: 10.1016/j.mex.2024.103095. eCollection 2025 Jun.
This research introduces the Generalized Extreme Value Mixture Autoregressive (GEVMAR) model as an innovative approach for examining non-standard actuarial datasets within general insurance. Information concerning claim reserves often reveals notable volatility and multimodal distributions, attributes that standard models, including previous method such as the Gaussian Mixture Autoregressive (GMAR) model and other autoregressive methodologies, find problematic to manage effectively. The GEVMAR model integrates the Generalized Extreme Value (GEV) distribution alongside Bayesian estimation techniques, augmented by a modified Signal-to-Noise Ratio (SNR) metric to improve predictive accuracy. Compared to preceding studies that adopted Gaussian-based or more elementary autoregressive models, the GEVMAR model displays a significantly elevated capacity to interpret complex data dynamics. The effectiveness of this methodological advancement has been rigorously assessed through its implementation to claim reserves data from insurance companies in Indonesia covering the period from 2015 to 2023, demonstrating that the GEVMAR model (GEV type I) consistently attains an improved adjusted SNR metric (1.3894 × 10⁶) coupled with a reduced Mean Absolute Percentage Error (MAPE) (0.0189) when compared to the GMAR model (MAPE 7.5812). Furthermore, the Bayesian methodology employed within the GEVMAR framework affords substantial versatility in incorporating prior distributions, thereby conferring a pivotal advantage in analyzing heavy-tailed datasets characterized by extreme variability. This study emphasizes the limitations of existing models, such as their reduced accuracy in capturing multimodal patterns and inability to address extreme volatility effectively. Some highlights of the proposed method are:•Development of a new model for the generalized extreme value mixture autoregressive.•Adjustment of SNR type 2 for the generalized extreme value mixture autoregressive model.•Application of the Bayesian GEVMAR (GEV type I) model to non-standard claim reserves data.
本研究引入广义极值混合自回归（GEVMAR）模型，作为一种用于检验一般保险中非标准精算数据集的创新方法。有关索赔准备金的信息往往显示出显著的波动性和多峰分布，而包括先前的高斯混合自回归（GMAR）模型等方法以及其他自回归方法在内的标准模型，难以有效处理这些特征。GEVMAR模型将广义极值（GEV）分布与贝叶斯估计技术相结合，并通过改进的信噪比（SNR）指标进行增强，以提高预测准确性。与之前采用基于高斯或更简单自回归模型的研究相比，GEVMAR模型在解释复杂数据动态方面具有显著更高的能力。通过将该方法应用于印度尼西亚保险公司2015年至2023年期间索赔准备金数据，对这一方法改进的有效性进行了严格评估，结果表明，与GMAR模型（平均绝对百分比误差（MAPE）为7.5812）相比，GEVMAR模型（I型GEV）始终能实现更高的调整后SNR指标（1.3894×10⁶）以及更低的平均绝对百分比误差（MAPE）（0.0189）。此外，GEVMAR框架中采用的贝叶斯方法在纳入先验分布方面具有很大的通用性，从而在分析具有极端变异性的重尾数据集方面具有关键优势。本研究强调了现有模型的局限性，例如它们在捕捉多峰模式方面准确性降低，以及无法有效应对极端波动性。所提出方法的一些亮点包括：
开发广义极值混合自回归新模型。
为广义极值混合自回归模型调整2型SNR。
将贝叶斯GEVMAR（I型GEV）模型应用于非标准索赔准备金数据。
