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Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting

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  • Yang Lu

Abstract

We study count processes in insurance, in which the underlying risk factor is time varying and unobservable. The factor follows an autoregressive gamma process, and the resulting model generalizes the static Poisson‐Gamma model and allows for closed form expression for the posterior Bayes (linear or nonlinear) premium. Moreover, the estimation and forecasting can be conducted within the same framework in a rather efficient way. An example of automobile insurance pricing illustrates the ability of the model to capture the duration dependent, nonlinear impact of past claims on future ones and the improvement of the Bayes pricing method compared to the linear credibility approach.

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  • 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.
    • Handle: RePEc:bla:jrinsu:v:85:y:2018:i:4:p:1083-1102
    DOI: 10.1111/jori.12190
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    Cited by:

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    3. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    4. Youn Ahn, Jae & Jeong, Himchan & Lu, Yang, 2021. "On the ordering of credibility factors," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 626-638.

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