Risk factor selection in rate making: EM adaptive LASSO for zero-inflated poisson regression models

Area of Science:

• Statistics
• Actuarial Science
• Data Science

Background:

• Risk factor selection is crucial for accurate insurance rate-making and understanding policyholder characteristics.
• Zero-inflated data, common in insurance claim frequency, pose significant challenges for traditional risk factor selection methods.
• Existing methods struggle to effectively handle the complexities introduced by excess zeros in insurance datasets.

Purpose of the Study:

• To propose a novel risk factor selection approach tailored for zero-inflated Poisson regression models.
• To address the difficulties in identifying significant risk factors within insurance data characterized by a high prevalence of zero claims.
• To enhance the precision of rate-making and the identification of high-value insureds through improved factor selection.

Main Methods:

• Development of the EM adaptive LASSO (Least Absolute Shrinkage and Selection Operator) method.
• Integration of the Expectation-Maximization (EM) algorithm with an adaptive LASSO penalty.
• Theoretical analysis demonstrating the selection consistency of the proposed method under regularity conditions.

Main Results:

• The EM adaptive LASSO method successfully selects important risk factors while excluding redundant ones with high probability.
• Simulation studies confirm the finite sample performance and effectiveness of the proposed approach.
• Application to car insurance data from the SAS Enterprise Miner database validates the method's practical utility.

Conclusions:

• The proposed EM adaptive LASSO offers a robust and effective solution for risk factor selection in zero-inflated insurance data.
• This method improves the accuracy of statistical modeling in insurance, leading to better risk assessment and pricing.
• The findings provide a valuable tool for actuaries and data scientists in the insurance industry for enhanced data analysis.