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Title: The Poisson-Lognormal regression model for mean and dispersion with an application to insurance ratemaking Authors:  Ryan Ho - London School of Economics (Singapore)
Natalia Hong - London School of Economics (United Kingdom) [presenting]
George Tzougas - London School of Economics and Political Science (United Kingdom)
Abstract: Within the actuarial field, the family of mixed Poisson models has been used extensively to model claim count data. The main focus is to present an extension of the Poisson-lognormal (PLN) regression model where both the mean and the dispersion parameters of the distribution are modelled as a function of explanatory variables. The adopted framework allows us to capture the stylized characteristics of the data in a more complete way. We propose a quite simple Expectation-Maximization type algorithm for maximum likelihood estimation of the model. Finally, a real data application using motor insurance data is examined and both the a priori and a posteriori, or Bonus-Malus, premium rates resulting from the model are compared to those determined by the Negative Binomial Type I and the Poisson-Inverse Gaussian regression models with regression structures on every parameter.