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Multivariate Credibility for Aggregate Loss Models

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  • Edward Frees

Abstract

Credibility is a form of insurance pricing that is widely used, particularly in North America. It is a special type of experience rating that employs a weighted average of claims experience and a previously established price to determine a new price for each risk class under consideration. This article extends traditional credibility formulas in two aspects. The new procedures are called “multivariate credibility” because both aspects make use of additional sources of data when compared to traditional formulas.Specifically, the first portion of the paper considers data from both the claims number and claims amount processes. Assuming an aggregate loss model for total claims, optimal insurance pricing formulas are derived. The insurance prices turn out to be an intuitively appealing weighted average of the overall mean claim, the claims number experience, and the claims amount experience. The second portion of the paper considers data from claims number and amount processes from multiple lines of business. By using covariances among lines of business (that are conditional on the unobserved heterogeneity), this article shows how to derive more efficient insurance prices.Accounting for covariance among different random quantities (securities) is standard practice in the investment industry. It is more difficult in an insurance context because of the heterogeneity associated with different risk classes. Nonetheless, ignoring this covariance has important ramifications, both theoretically and practically. For an illustrative sample of Massachusetts automobile claims, we show that the relative differences in accounting for and ignoring the covariance range from −3.9% to 14.5% for a selected bundle of insurance coverages.

Suggested Citation

  • Edward Frees, 2003. "Multivariate Credibility for Aggregate Loss Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(1), pages 13-37.
  • Handle: RePEc:taf:uaajxx:v:7:y:2003:i:1:p:13-37
    DOI: 10.1080/10920277.2003.10596074
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    Citations

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    Cited by:

    1. Marina Maniati & Evangelos Sambracos, 2017. "Decision-making process in shipping finance: A stochastic approach," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1317083-131, January.
    2. Oh, Rosy & Lee, Youngju & Zhu, Dan & Ahn, Jae Youn, 2021. "Predictive risk analysis using a collective risk model: Choosing between past frequency and aggregate severity information," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 127-139.
    3. Yang Lu, 2018. "Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 1083-1102, December.
    4. Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2018. "Multivariate Credibility in Bonus-Malus Systems Distinguishing between Different Types of Claims," Risks, MDPI, vol. 6(2), pages 1-11, April.
    5. Levon Barseghyan & Francesca Molinari & Darcy Steeg Morris & Joshua C. Teitelbaum, 2020. "The Cost of Legal Restrictions on Experience Rating," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 17(1), pages 38-70, March.
    6. Joanna Sawicka, 2013. "Model stochastycznej zależności liczby szkód i wartości pojedynczej szkody," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 157-183.
    7. Bladt, Martin & Yslas, Jorge, 2023. "Robust claim frequency modeling through phase-type mixture-of-experts regression," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 1-22.
    8. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.

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