Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

Lluís Bermudez (lbermudez@ub.edu) and Dimitris Karlis (karlis@aueb.gr)
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Lluís Bermudez: Departament de Matemµatica Econµomica, Financera i Actuarial, Universitat de Barcelona
Dimitris Karlis: Athens University of Economics and Business

No XREAP2010-04, Working Papers from Xarxa de Referència en Economia Aplicada (XREAP)

Abstract: When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce di®erent multivariate Poisson regression models in order to relax the independence assumption, including zero-in°ated models to account for excess of zeros and overdispersion. These models have been largely ignored to date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

Keywords: Multivariate Poisson regression models; Zero-inflated models; Automobile insurance; MCMC inference; Gibbs sampling (search for similar items in EconPapers)
JEL-codes: C51 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2010-04, Revised 2010-04
New Economics Papers: this item is included in nep-ecm and nep-ias
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http://www.xreap.cat/RePEc/xrp/pdf/XREAP2010-4.pdf First version, 2010 (application/pdf)
http://www.xreap.cat/RePEc/xrp/pdf/XREAP2010-4.pdf Revised version, 2010 (application/pdf)

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