Mixture of bivariate Poisson regression models with an application to insurance

Lluís Bermúdez () and Dimitris Karlis
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Lluís Bermúdez: Departament de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Diagonal 690, 08034-Barcelona, Spain.
Dimitris Karlis: Athens University of Economics and Business, Greece.

No XREAP2011-10, Working Papers from Xarxa de Referència en Economia Aplicada (XREAP)

Abstract: In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models 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, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Keywords: Zero-inflation; Overdispersion; EM algorithm; Automobile insurance; A priori ratemaking. (search for similar items in EconPapers)
JEL-codes: C51 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2011-07, Revised 2011-07
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http://www.xreap.cat/RePEc/xrp/pdf/XREAP2011-10.pdf First version, 2011 (application/pdf)
http://www.xreap.cat/RePEc/xrp/pdf/XREAP2011-10.pdf Revised version, 2011 (application/pdf)

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