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Mathematical modelling in general insurance
 Zajíček, Jakub ; Bílková, Diana (advisor) ; Bohatová Chládková, Dana (referee)
This diploma thesis deals with the mathematical models in general insurance. The aim of this thesis is to analyse selected mathematical models that are widely used in general insurance for the estimation of insurance portfolio statistics, pricing and the regulatory capital requirement calculation. Claim frequency models, claim severity models, aggregate loss models and generalized linear models are analysed. This thesis consists of a theoretical and a practical part. The theoretical part contains description of selected models. Described models are then applied to a real dataset in the practical part. The real dataset modelling was performed using the statistical software R. It has been proved that maximum likelihood parameter estimations are of better quality than the method of moments or quantile method estimations. The results of aggregate loss distribution computational methods are comparable. This comparability is mostly caused by a large number of observations. In the context of tariff analysis it was found that the most significant factors are driver's age and the driver's area of residence.
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