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

Area of Science:

• Actuarial science
• Statistical modeling
• Risk management

Background:

• Standard models struggle with volatile and multimodal insurance claim reserve data.
• Existing autoregressive and Gaussian Mixture Autoregressive (GMAR) models have limitations in capturing complex data dynamics.

Purpose of the Study:

• Introduce the Generalized Extreme Value Mixture Autoregressive (GEVMAR) model for non-standard actuarial datasets.
• Enhance predictive accuracy for insurance claim reserves using a modified Signal-to-Noise Ratio (SNR) metric.
• Address the limitations of current models in handling extreme volatility and multimodal distributions.

Main Methods:

• Developed the Generalized Extreme Value Mixture Autoregressive (GEVMAR) model, integrating Generalized Extreme Value (GEV) distribution with Bayesian estimation.
• Applied a modified Signal-to-Noise Ratio (SNR) metric for improved predictive accuracy.
• Utilized Bayesian techniques for enhanced versatility in analyzing heavy-tailed datasets.

Main Results:

• The GEVMAR model (GEV type I) demonstrated superior performance on Indonesian insurance claim reserves data (2015-2023).
• Achieved an improved adjusted SNR metric (1.3894 × 10⁶) and a reduced Mean Absolute Percentage Error (MAPE) of 0.0189 compared to the GMAR model (MAPE 7.5812).
• The Bayesian approach facilitated effective analysis of datasets with extreme variability.

Conclusions:

• The GEVMAR model offers a significant advancement for analyzing complex, non-standard actuarial data, particularly claim reserves.
• It overcomes the limitations of traditional models in managing data volatility and multimodal patterns.
• The proposed methodology provides a more accurate and versatile tool for actuarial risk assessment.