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Modelling the Loss Development in Time with Aid of Copulas
Obdržálková, Ludmila ; Šváb, Jan (advisor) ; Justová, Iva (referee)
There is proposed and described stochastic approach of calculation of IBNR reserve based on modelling loss development in time using copulas in this thesis. The first chapter determinates basic terms of copula theory and gives compact summary of most widely known copula families. Particular steps of calculation of IBNR reserve follow in the second chapter. The calculation is demonstrated numerically over the casco insurance. The resultant distribution is compared with distribution obtained by Mack's model for the Chain ladder method.
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Insurance contracts clustering to risk homogenous groups
Martínek, Jan ; Zimmermann, Pavel (advisor) ; Justová, Iva (referee)
In the present work we study classes of homogenous policy contracts by CEIOPS definition and its specified risk characteristics. First part of the thesis study the risk measures and the methods used to measure these risks. As the main risk categories we study underwriting and reserve risk. In the second part of the thesis we analyse these classes by its risk characteristics and cluster them in homogenous groups. At the end we outline the characteristic features of each group for better understanding the result of presented cluster analysis.
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Claims reserve calculation for data separating true IBNR and IBNER
Šťástka, Petr ; Mazurová, Lucie (advisor) ; Justová, Iva (referee)
The thesis deals with calculating technical reserves of non-life insurance undertakings, especially calculating the claims reserve, which is the most important non-life insurance reserve. It describes the reserve for claims in detail focusing consequently on the different calculation methods. The thesis focuses particularly on the description of the model proposed by the Swiss mathematician René Schnieper. This is a special model aimed at estimating the ultimate claims based on the decomposition of the incurred data into new claims amounts and changes in incurred amounts for the existing claims reported in the earlier years of the development. The final chapter numerically illustrates and compares the methods mentioned in this thesis.
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The analysis of approximations of technical reserves in Solvency II
Kvardová, Lucie ; Justová, Iva (advisor) ; Mandl, Petr (referee)
In the present work we study the alternatives in the valuation of technical provisions under the Solvency II. We are concerned on set of proposals which are about the usage of proxies released in the fourth Quantitative Impact Study. The proxy is an approach for the calculation of the best estimate for those companies which do not have the sufficient statistical data in order to carry out a proper actuarial calculation. This work is based on application of proxy to the traditional actuarial techniques. There is also a description of supervisors procedure how to derive market parameters based on claims development scheme of each insurance company. The next chapter is focused on model error calculation and gives us an information whether the proxy method is proper and reliable. There is also a need of risk margin calculation to meet the insurers obligations. This work also enumerates a number of risk margin's proxies.
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Non-proportional Reinsurance in Solvency II
Havlíková, Tereza ; Justová, Iva (advisor) ; Mazurová, Lucie (referee)
Title: Non-proportional Reinsurance in Solvency II Author: Tereza Havlíková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Iva Justová, Ph.D. Supervisor's e-mail address: iva justova@hotmail.com Abstract: The aim of this thesis is to analyse non-proportional reinsurance of non-life insurance. Taking into account the latest Quantitative Impact Study QIS 5, we calculate the capital requirement under Solvency II and we focus on the premium and reserve risk. The first part of this work describes basic concepts and formulas. Furthermore, in the main part we describe the standard formula for the calculation of the capital requirement from which we derive a formula for the calculation of the capital requirement but this time taking into account the impact of reinsurance. In the last chapter, we apply the approach on an example, in which we examine the influence of parameters on the capital requirement. Keywords: non-proportional reinsurance, Solvency II, non-life underwriting risk 1
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