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Prediction error in non-life claims reserves
Divišová, Kateřina ; Justová, Iva (advisor) ; Mandl, Petr (referee)
This thesis deals with a description of three claims reserving methods - with stochastic models for Chain ladder, Bornhuetter/Ferguson and multiplicative method. There are mentioned their assumptions, parameter estimates, their properties and formulas for loss reserves in the first part. The second part of the text is devoted to formulas for the mean squared error of prediction and its estimate. Finally, a numerical example shows comparison of these methods.
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Prediction error for mixed models
Šlampiak, Tomáš ; Komárek, Arnošt (advisor) ; Hlávka, Zdeněk (referee)
A Linear mixed-effects model (LME) is one of the possible tools for longitudinal or group--dependent data. This thesis deals with evaluating of prediction error in LME. Firstly, it is derived the mean square error of prediction (MSEP) by direct calculation. Then the covariance penalty method and crossvalidation is presented for evaluation of MSEP in LME. Further, it is shown how Akaike information criterion (AIC) can be used in mixed-effects models. Because of the model's properties two types of AIC are distinguished - marginal and conditional one. Subsequently, the procedures of AIC's calculation and its basic asymptotic properties are described. Finally, the thesis contains simulation study of behaviour of marginal and conditional AIC with the goal to choose the right variance structure of random effects. It turns out that the marginal criterion tends to select models with smaller number of random effects than conditional criterion.
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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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Prediction error in non-life claims reserves
Divišová, Kateřina ; Justová, Iva (advisor) ; Mandl, Petr (referee)
This thesis deals with a description of three claims reserving methods - with stochastic models for Chain ladder, Bornhuetter/Ferguson and multiplicative method. There are mentioned their assumptions, parameter estimates, their properties and formulas for loss reserves in the first part. The second part of the text is devoted to formulas for the mean squared error of prediction and its estimate. Finally, a numerical example shows comparison of these methods.
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