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

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  • Shengkun Xie

    (Global Management Studies, Ted Rogers School of Management, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada)

  • Chong Gan

    (Global Management Studies, Ted Rogers School of Management, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada)

Abstract

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.

Suggested Citation

  • Shengkun Xie & Chong Gan, 2025. "Modeling Age-to-Age Development Factors in Auto Insurance Through Principal Component Analysis and Temporal Clustering," Risks, MDPI, vol. 13(6), pages 1-19, May.
    • Handle: RePEc:gam:jrisks:v:13:y:2025:i:6:p:100-:d:1661589
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    References listed on IDEAS

    as
    1. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    2. Peng Shi & Brian M. Hartman, 2016. "Credibility in Loss Reserving," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(2), pages 114-132, April.
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