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Classification Ratemaking
Valášková, Zuzana ; Mazurová, Lucie (advisor) ; Mandl, Petr (referee)
In the present work we will study methods, which are used to find a premium in nonlife insurance according to the grouping risks into the risk groups. These risk groups are constructed according to the concrete indices. All work consists of the three main sections. At the end you can find example, where all methods are applied. First section explains the basic methods which can be used in ratemaking: the weighted least square method, the method of marginal totals and the method of Bailey - Simon. The second section studies more sophisticated method for ratemaking: The generalized linear models. The third section studies the credibility estimations used in ratemaking, which are important and used today.
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Multidimensional Bonus Malus Systems in Non-life Insurance
Drábková, Miroslava ; Mandl, Petr (advisor) ; Mazurová, Lucie (referee)
Bonus-malus systems are tariff systems which determine premium depending on clairn history of insured risks in previous periods. The thesis deals with computation of part of risk which falls on policy holders and on insurance company. There is used the Bayesian approach in the first part. A portfolio is assumed in which the risk parameter of each policy holder is a random variable. There is established a model with two kinds of policy holders too, every kind has a given distribution of the risk parameter again. There are mentioned some bonus-malus systems used in the world in third-party liability insurance in the second part. It is shown how to modify the systems which do not satisfy the Markovian condition to a model which satisfies this condition. It is useful for next calculations. A portfolio is assumed again in which the risk parameter of each policy holder is a random variable and it is computed part of risk which falls on policy holders and on insurance company. The calculations are supplemented by concrete numerical iII ustrations.
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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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Risk Margins in the Liability Adequacy Test for Life Insurance
Sotona, Petr ; Senft, Tomáš (advisor) ; Mandl, Petr (referee)
In the present thesis we study risk margins in the liability adequacy test for life insurance. First we look at the theory of risk margins and liability adequacy test. We discuss desirable characteristics of the risk margins and the methods used to their evaluation. We show risk margins from di erent aspects and views as well. In second part of the thesis we introduce the model of product for endowment and we describe contractual cash flows. We also construct generation mortality tables for use in described model. Afterwards we evaluate risk margin for mortality risk using stochastic modelling. Finally we compare calculated risk margin with value of the margin calculated by current approach recommended to calculation of LAT in the Czech Republic and analyse results.
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