Stochastic reserving methods in non-life insurance
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The aim of the present thesis is to describe the classical basic chain-ladder method and several stochastic methods. The thesis is set out as follows. First section starts with the notation and basic results. It is followed by the overview and description of the chain-ladder technique. The section continues with the Mack’s stochastic model, where the model assumptions and the results of calculating the variability are given. Section 2 provides an introduction to stochastic models in the basis of generalized linear models (GLM). Discussion starts with the (over-dispersed) Poisson model and since there are several models linked to Poisson model, these models are examined as well. The stochastic models are introduced with the ideas of constructing the models and since the main focus is on estimating the likely variability of the estimate, the results of prediction errors are given. In section 3, the models considered in the previous chapter, will be compared. As the Mack’s distribution-free model and the Poisson model are considered as the chain-ladder "type" methods, it is important to point out the main differences of these models. The comparison leads to the known fact, that the distributin-free model of Mack is called as the stochastic model underlying the chain-ladder method. In addition, discussion about possible negative increments and how the proposed methods deal with them is provided. The last section provides a practical reserving approach. The theoretical results considered in previous sections are implemented in a practical numerical problem, the reserve estimates and their mean square errors (and standard errors) of predictions are found for models of Mack, over-dispersed Poisson, log-normal and Gamma.