On the Bayesian generalized extreme value mixture autoregressive model with adjusted SNR in non-standard actuarial data.

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.