Modelagem glm aplicada à atuária: uma utilização dos modelos lineares generalizados na precificação de seguros

Abstract

The Generalized Linear Models – GLMs – introduced initially by the British actuaries Nelder and Wedderburn (1972) corresponds to a synthesis of a large set of existing linear regression models. This class of models is an extension to classical linear regression model taking into account the fact that GLMs not restrict the choice of the probability distribution of the response variable, in which case the classical linear model must necessarily be a normal distribution. Thus, in order to develop a pricing model for a non-life insurance, it was decided here resort to using the GLM modeling because of the empirical distribution of the data analyzed in safe distance themselves substantially from the assumptions adopted classical linear model, as the normality of the observations and the residuals, homocedasticity, among others. In this context the pricing of insurance, GLMs were applied to data on the frequency and severity of claims in the present dataset moped insurance Ohlsson and Johansson (2010). Through GLMs was possible to fit two models, one for the average number and other for the average value of claims, estimating from these the coefficients and the relativities components of the calculation model for the risk premium. Also, the best fit obtained for the frequency of the claims was the Log-Poisson model, while for the severity was the Log-Gaussian Inverse model. Finally it was analyzed in that direction, and in that intensity, the tariff variables affecting the calculation of the insurance premium, thereby allowing generate, objectively, estimates a priori about the premium to be calculed for each policy based on profile individual risk of the insured.