On the Importance of Dispersion Modeling for Claims Reserving: An Application with the Tweedie Distribution

By Jean-Philippe Boucher, Danail Davidov

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We consider Tweedie’s compound Poisson model in a claims reserving triangle in a generalized linear model framework. We show that there exist practical situations where the variance, as well as the mean of the costs, needs to be modeled. We optimize the likelihood function through either direct optimization or through double generalized linear models (DGLM). We also enhance the estimation of the variance parameters within the DGLM by using the restricted maximum likelihood (REML). Having a flexible variance structure allows the model to replicate the underlying risk more appropriately and shrinks the gap between the predicted variances of different models.

Keywords: Claims reserves, incurred but not reported, mean square error of prediction, Tweedie, compound Poisson model, exposure, generalized linear model, dispersion, double generalized linear model (DGLM), power variance function, restricted maximum likelihood, saddle-point approximation

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Boucher, Jean-Philippe, and Danail Davidov, "On the Importance of Dispersion Modeling for Claims Reserving: An Application with the Tweedie Distribution," Variance 5:2, 2011, pp. 158-172.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.