Model Misspecification and Data-Driven Model Ranking Approach for Insurance Loss and Claims Data

Statistical models are crucial in analyzing insurance loss and claims data, offering insights into various risk elements. The prevailing statistical notion that “all models are wrong, but some are useful” can wield significant influence, particularly when multiple competing statistical models are considered. This becomes particularly pertinent when all models portray similar characteristics within specific subsets of the support of the random variable under scrutiny. Since the actual model is unknown in practical scenarios, the challenge of model selection becomes daunting, complicating the study of associated characteristics of the actual data generation process. To address these challenges, the concept of model averaging is embraced. Often, averaging over multiple models helps alleviate the risk of model misspecification, as different models may capture distinct aspects of the data or modeling assumptions. This enhances the robustness of the estimation process, yielding a more accurate and reasonable estimate compared to relying solely on a single model. This paper introduces two novel data-based model selection methods—one using the likelihood function and the other using the density power divergence measure. The study focuses on estimating the Value-at-Risk (VaR) for non-life insurance claim size data, providing comprehensive insights into potential losses for insurers. The performance of the proposed procedures is evaluated through Monte Carlo simulations under both uncontaminated conditions and in the presence of data contamination. Additionally, the applicability of the methods is illustrated using two real non-life insurance datasets, with the VaR values estimated at different confidence levels.