Modelling dependence in a ratemaking procedure with multivariate Poisson regression models
AbstractWhen 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Xarxa de Referència en Economia Aplicada (XREAP) in its series Working Papers with number XREAP2010-04.
Length: 40 pages
Date of creation: Apr 2010
Date of revision: Apr 2010
Contact details of provider:
Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques i Empresarials, Universitat de Barcelona, c/ Tinent Coronel Valenzuela, 1-11, 08034 Barcelona
Web page: http://www.pcb.ub.edu/xreap
More information through EDIRC
Multivariate Poisson regression models; Zero-inflated models; Automobile insurance; MCMC inference; Gibbs sampling;
Find related papers by JEL classification:
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-10-30 (All new papers)
- NEP-ECM-2010-10-30 (Econometrics)
- NEP-IAS-2010-10-30 (Insurance Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- van Ophem, Hans, 1999. "A General Method To Estimate Correlated Discrete Random Variables," Econometric Theory, Cambridge University Press, vol. 15(02), pages 228-237, April.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: () The email address of this maintainer does not seem to be valid anymore. Please ask to update the entry or send us the correct address.
If references are entirely missing, you can add them using this form.