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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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Long-Term Insurance and Permanent Health Insurance
Kočová, Karolína ; Cipra, Tomáš (advisor) ; Šváb, Jan (referee)
This thesis deals with long-term care insurance and disability insurance. Both products are classified as products of private health insurance which is described in the first chapter. We can find characteristics of longterm care and its providers in Czech republic in the second chapter. Further, some numerical methods used in long-term care insurance are stated. The third chapter describes the British model of length of stay in institutional long-term care, the results of the study in the Great Britain are summarized in brief. The fourth chapter deals with characteristics and numerical methods of disability insurance. The fifth chapter displays the use of state model in disability insurance. The emerging costs method is illustrated on simple example. The life tables for disabled people were designed to be used in the calculation. In the conclusion we can find reasoning for the future of products mentioned above on the Czech insurance market.
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The Bornhuetter-Ferguson method, parameter estimation and prediction error
Santnerová, Petra ; Šváb, Jan (advisor) ; Mazurová, Lucie (referee)
This diploma thesis describes the Bornhuetter-Ferguson method, which is used to calculate the IBNR reserve. It is divided into deterministic and stochastic parts. The deterministic part deals with the derivation of development pattern and ultimate loss amount, which are needed to calculate the reserve. The stochastic part deals with reserve estimation error and prediction error. The calculation results of the reserve estimate and its error are compared with the results of the chain ladder method. The last chapter deals with the problematic areas of the described method.
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Long-Term Insurance and Permanent Health Insurance
Kočová, Karolína ; Šváb, Jan (referee) ; Cipra, Tomáš (advisor)
This thesis deals with long-term care insurance and disability insurance. Both products are classified as products of private health insurance which is described in the first chapter. We can find characteristics of longterm care and its providers in Czech republic in the second chapter. Further, some numerical methods used in long-term care insurance are stated. The third chapter describes the British model of length of stay in institutional long-term care, the results of the study in the Great Britain are summarized in brief. The fourth chapter deals with characteristics and numerical methods of disability insurance. The fifth chapter displays the use of state model in disability insurance. The emerging costs method is illustrated on simple example. The life tables for disabled people were designed to be used in the calculation. In the conclusion we can find reasoning for the future of products mentioned above on the Czech insurance market.
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Modelling the Loss Development in Time with Aid of Copulas
Obdržálková, Ludmila ; Justová, Iva (referee) ; Šváb, Jan (advisor)
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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