A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

Bivariate Poisson regression models for ratemaking in car insurance have been previously used. They included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. These models are now revisited in order to consider alternatives. A 2-finite mixture of bivaria...

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Bibliographic Details
Authors: Bermúdez, Lluís, Karlis, Dimitris
Format: article
Status:Versión aceptada para publicación
Publication Date:2012
Country:España
Institution:Universidad de Barcelona
Repository:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/106474
Online Access:https://hdl.handle.net/2445/106474
Access Level:Open access
Keyword:Inflació
Anàlisi de regressió
Assegurances d'accidents
Variables (Matemàtica)
Inflation
Regression analysis
Accident insurance
Variables (Mathematics)
Description
Summary:Bivariate Poisson regression models for ratemaking in car insurance have been previously used. They included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. These models are now revisited in order to consider alternatives. A 2-finite mixture of bivariate Poisson regression models is used to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, it is shown that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Finally, an EM algorithm is provided in order to ensure the models' ease-of-fit. These models are applied to an automobile insurance claims data set and it is shown that the modeling of the data set can be improved considerably.