Title: The negative binomial inverse Gaussian regression model with an application to insurance ratemaking
Authors: George Tzougas - London School of Economics and Political Science (United Kingdom) [presenting]
Jun Ming Lim - London School of Economics and Political Science (United Kingdom)
Wei Li Hoon - London School of Economics and Political Science (United Kingdom)
Abstract: The aim of this study is to propose the Negative Binomial-Inverse Gaussian (NBIG) regression model as a competitive alternative to mixed Poisson regression models that have been widely used for actuarial purposes. The Negative Binomial-Inverse Gaussian regression model can be considered as a candidate model for highly dispersed count data and this is the first time that it is used in a statistical or an actuarial setting. Specifically, the main contribution of this work is that it illustrates that Maximum Likelihood (ML) estimation of the Negative Binomial-Inverse Gaussian regression model can be accomplished rather easily via an Expectation Maximization (EM) type algorithm. Moreover, the EM scheme we propose can be employed to estimate other members of the mixed Negative Binomial family as it can address situations where the mixing distribution is not conjugate to the Negative Binomial distribution. Furthermore, the a prori and a posteriori, or Bonus-Malus, premium rates resulting from the NBIG model are compared to those determined by the Negative Binomial Type I (NBI) and the Poisson-Inverse Gaussian (PIG) regression models that have been traditionally used for a priori and a posteriori ratemaking.