Modeling Age-to-Age Development Factors in Auto Insurance Through Principal Component Analysis and Temporal Clustering

The estimation of age-to-age development factors is fundamental to loss reserving, with direct implications for risk management and regulatory compliance in the auto insurance sector. The precise and robust estimation of these factors underpins the credibility of case reserves and the effective management of future claim liabilities. This study investigates the underlying structure and sources of variability in development factor estimates by applying multivariate statistical techniques to the analysis of development triangles. Departing from conventional univariate summaries (e.g., mean or median), we introduce a comprehensive framework that incorporates temporal clustering of development factors and addresses associated modeling complexities, including high dimensionality and temporal dependency. The proposed methodology enhances interpretability and captures latent structures in the data, thereby improving the reliability of reserve estimates. Our findings contribute to the advancement of reserving practices by offering a more nuanced understanding of development factor behavior under uncertainty.