Advanced statsitical methods in non-life insurance reserving

Reserving has always been an important task for insurance companies. With the adoption of Solvency II directive, development of stochastic modelling for that purpose is becoming increasingly important as uncertainty of the predictions is legally required. The generalized linear model (GLM) is a popular method used for claims reserving, however, there is a need for development of models with more sophisticated correlation structures without the restrictive assumption of independence of incremental claims. This thesis implements the generalized linear mixed model (GLMM) on aggregated insurance dataset using more than one random effect. Both the theory behind GLM and GLMM as well reserving theory were discussed. Practical application of one GLM and three different GLMM models on a real dataset and their further comparison and diagnostics were carried out. The goal was to find the structure of the model best suited for the given dataset measured using several criteria.