Mixture of bivariate Poisson regression models with an application to insurance
Bermúdez, Lluís (Universitat de Barcelona. Departament de Matemàtica Financera i Actuarial)
Karlis, Dimitris (Athens University of Economics and Business)
Xarxa de Referència en Economia Aplicada (XREAP)

Imprint: Xarxa de Referència en Economia Aplicada (XREAP) 2011
Description: 34 p.
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.
Rights: Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i la xarxa i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús Creative Commons
Language: Anglès.
Series: Documents de treball de la Xarxa de Referència en Economia Aplicada (XREAP)
Series: XREAP ; 2011-10
Document: workingPaper
Subject: Zero-inflation ; Overdispersion ; EM algorithm ; Automobile insurance ; A priori ratemaking ; Regression analysis ; Assegurances d'automòbils ; Anàlisi de regressió

Adreça alternativa: http://hdl.handle.net/2072/152176

34 p, 450.0 KB

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Research literature > Studies

 Record created 2012-08-31, last modified 2017-10-21

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