A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component

Abstract

The objective of this paper is to provide an extension of well-known models of tarification in automobile insurance. The analysis begins by introducing a regression component in the Poisson model in order to use all available information in the estimation of the distribution. In a second step, a random variable is included in the regression component of the Poisson model and a negative binomial model with a regression component is derived. We then present our main contribution by proposing a bonus-malus system which integrates a priori and a posteriori information on an individual basis. We show how net premium tables can be derived from the model. Examples of tables are presented.

A copula approach to test asymmetric information with applications to predictive modeling

“…These pure premiums can further assist the insurer to investigate financial adequacy. While it will be more appealing to examine the claims within a longitudinal context, for example, Dionne and Vanasse (1989), Pinquet et al (2001), Bolancé et al (2003), and Pinquet (1997Pinquet ( , 1998, we leave this for future work. Comprehensive reviews of statistical models for experience rating in insurance can be found in Pinquet (2000) and Gouriéroux and Jasiak (2007).…”

Discrete distributions when modeling the disability severity score of motor victims

“…then the mixture will result in a NB distribution with probability distribution: 1920; for extensions designed to include exogenous data and an application to accident data, see Lawless, 1987;and Dionne and Vanasse, 1989). The second equality in ( …”

Copula credibility for aggregate loss models

“…The regression coefficients and the serial correlation parameters can be estimated via a method of moments approach such as generalized estimating equations. This is the approach used by Dionne and Vanasse (1989) and Pinquet and co-authors. 2.…”

“…Within the actuarial literature, Dionne and Vanasse (1989) led applications by applying a random effects Poisson count model to automobile insurance claims. Here, a (time-constant) latent variable was used to represent heterogeneity among claims, which implicitly also induces a constant correlation over time.…”