Generalised linear models for aggregate claims: to Tweedie or not?

Abstract

The compound Poisson distribution with gamm a claim sizes is a very common model for premium estimation in Property and Casualty insurance. Under this distributional assumption, generalised linear models (GLMs) are used to estimate the mean claim frequency and severity, then these estimators are simply multiplied to estimate the mean aggregate loss. The Tweedie distribution allows to parametrise the compound Poisson-gamma (CPG) distribution as a member of the exponential dispersion family and then fit a GLM with a CPG distribution for the response. Thus, with the Tweedie distribution it is possible to estimate the mean aggregate loss using GLMs directly, without the need to previously estimate the mean frequency and severity separately. The purpose of this educational note is to explore the differences between these two estimation methods, contrasting the advantages and disadvantages of each.

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Acknowledgments

The authors are sincerely grateful to the Editor, Co-Editor and an anonymous referee for their constructive comments that helped improve this educational note.

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Correspondence to Oscar Alberto Quijano Xacur.

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The authors gratefully acknowledge the partial financial support of NSERC Grant 36860-2012.

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Quijano Xacur, O.A., Garrido, J. Generalised linear models for aggregate claims: to Tweedie or not?. Eur. Actuar. J. 5, 181–202 (2015). https://doi.org/10.1007/s13385-015-0108-5

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Keywords

  • Tweedie distribution
  • GLMs
  • Exponential dispersion family