Generalized linear models and generalized linear mixed models – A theoretical and practical presentation with application to motor insurance

Specialeforsvar ved Dora Kristin Fransdottir

Titel: Generalized linear models and generalized linear mixed models – A theoretical and practical presentation with application to motor insurance

Resume:  Generalized linear models (GLM) have become a frequent used statistical tool for modelling insurance data, dating back to the test by McCullagh and Nelder (1989). Traditional linear models are used for modelling relationships between observed random variables, Y, and a number of covariates, also called explanatory variables. The GLM generalizes the classical  linear model by including response distributions from the exponential family and models the additive effect of explanatory variables on a transformation of the mean, instead of the mean itself. A standard GLM requires the response variable to be independent samples. This is not always true for actuarial data, for example with longitudinal data where there are repeated measures on the same subject over a time period. In these cases the observations can share subject characteristics over time and be substantively correlated. An extension of the GLM that takes this correlation into account, is the generalized linear mixed models (GLMM). For distributions from the exponential family, the GLMM extends the GLM by including a random effect in the linear predictor, i.e. in the structure for the mean. This thesis describes the theory for the GLM and GLMM respectively. The models are then used on data provided by the Icelandic insu-rance company VÍS. The data contained three covers from the motor insurance product 4010 containing covers 1411a, 1412a and 1421b. The cover 1411a contained both bodily claims and property damages, and were therefore split into two subcovers, 1411a L for the bodily claims and 1411a M for the property damages. The cover 1412a contained bodily claims and the cover 1421b property damages. A total of four covers were therefore considered. The estimated parameters for the explanatory variables, from both models for each of the four covers, were then used to calculate a new tariff

Vejledere :  Jostein Paulsen, Thorir Oskarsson
Censor:        Mette M Havning