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State space modeling of run-off triangles
Kohout, Marek ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee)
The main goal of this Diploma thesis is to describe an approach for modeling run-off triangles of nonlife insurance (calculation of IBNR reserve) based on state space models and apply the method to the selected run-off triangles. In difference from (Atherino a kol., 2010) the KFAS package in R software is used for modeling purposes in the numerical study at the end of the thesis. One provides a preview of various possibilities of data and model adjustment applied to the same run-off triangles in order to asses added value of these steps (logartihmic transformation of input data, interventions for outliers etc.). A special attention is devoted to lognormal modification of the basic state space model. An integral part of the numerical study in the thesis is a residual diagnostic of models and simulation approach to IBNR reserves. 1
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Reserving in Non-Life Insurance
Těšínský, Jiří ; Gerthofer, Michal (advisor) ; Zimmermann, Pavel (referee)
This thesis deals with reserving issues in non-life insurance. The main aim is to compare methods used to estimate outstanding claims reserves and delineate their advantages, disadvantages, extensions and limitations. Initially, in the theoretical section, there are mathematically formulated chosen models and their assumptions, which are then applied to real data in the practical section. Finally, the findings acquired from both parts are utilized for the comparison of applicability of methods and the identification of their further distinctions and commonalities.
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Variability estimation of development triangles in nonlife insurance
Havlíková, Tereza ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
The aim of this thesis is to describe calculation methods for variability esti- mation of claims reserve in non-life insurance. The thesis focuses on three main categories of models: Mack's stochastic Chain-Ladder, generalized linear models and bootstrap. Both the theoretical and also the empirical parts are included. Empirical part is devoted to application of all the models described above on both real and simulated data. 1
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