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Variable life annuity
Šimlovič, Matej ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
In the first chapter, the thesis contains a description of variable annuity and description of four basic guarantees: guaranteed minimum death benefit, guaranteed minimum accumulation benefit, guaranteed minimum income bene- fit and guaranteed minimum withdrawal benefit. For each of these guarantees, there is a description of principle of the benefit, assumptions of payment, amount of payment and a difference from a product without such guarantee, thus a net benefit from the guarantee. In the second chapter, with additional assumptions, there are deductions of expected values of benefits from the described guaran- tees and numerical calculation of these expected values for both genders, various entering ages and various investment variables. 1
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Financing post-retirement income
Skřivanová, Zuzana ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
This thesis deals with various possibilities of the financing post-retirement income. In the first part, the basic knowledge from the area of demography is given, what is necessary for the determination of mortality assumptions and for the computation of cash flows in post-retirement age. Subsequently models of decumulation periods are theoretically compared - the basic variants are purchasing of life annuity and annuity-certain, from which are derived selected combinations and modifications. In the last part, theoretical bases are used to determining specific mortality assumptions with respect to the computed values of parameters of the Gompertz-Makeham mortality law. Subsequently cash flows of particular models are numerically illustrated with respect to the mortality assumptions.
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Multi - event Bonus - Malus System
Kaplanová, Martina ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
This work deals with bonus - malus systems for automobile insurance that distinguishtypes of claim. The first part of this work is definition of bonus - malus systems that do not distinguish types of claim and then their expansion just to multi - event bonus - malus systems. The main focus of the work is computation of stationary distribution for different systems, which means the distribution of classes in which the system stabilizes. Furthermore, there are several simulations of trajectory of insured through the system based on the number and type of accidents that they have caused. Finally, relative frequencies of classes in which insured is at the end of the simulation and the stationary distribution of the system are compared. Powered by TCPDF (www.tcpdf.org)
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Modern stochastic claims reserving methods in insurance and their comparison
Vosáhlo, Jaroslav ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
This thesis deals with an issue of claims reserving for non-life insurance. The issue is approached in a sense of analytical calculation and stochastic modelling. First, Chain-ladder, Bornhuetter-Ferguson, Benktander-Hovinen and Cape-Cod method are introduced. In following chapters, we try to find related stochastic underlying models including Generalized linear models and Mack's distribution-free approaches, we analyze second moments of claims estimates for each of the methods and examine alternative Merz-Wüthrich approach to reserve risk measurement. At the end, bootstrap algorithm and estimates are suggested and simulation results are compared with analytic ones.
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Extreme Value Theory in Actuarial Sciences
Jamáriková, Zuzana ; Mazurová, Lucie (advisor) ; Antoch, Jaromír (referee)
This thesis is focused on the models based on extreme value theory and their practical applications. Specifically are described the block maxima models and the models based on threshold exceedances. Both of these methods are described in thesis theoretically. Apart from theoretical description there are also practical calculations based on simulated or real data. The applications of block maxima models are focused on choice of block size, suitability of the models for specific data and possibilities of extreme data analysis. The applications of models based on threshold exceedances are focused on choice of threshold and on suitability of the models. There is an example of the model used for calculations of reinsurance premium for extreme claims in the case of nonproportional reinsurance.
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Modelling Bonus - Malus Systems
Stroukalová, Marika ; Mazurová, Lucie (advisor) ; Prokešová, Michaela (referee)
Title: Modelling Bonus - Malus Systems Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., KPMS MFF UK Abstract: In this thesis we deal with bonus-malus tariff systems commonly used to adjust the a priori set premiums according to the individual claims during mo- tor third party liability insurance. The main aim of this thesis is to describe the standard model based on the Markov chain. For each bonus-malus class we also determine the relative premium ("relativity"). Another objective of this thesis is to find optimal values for the relativities taking into account the a priori set premiums. We apply the theoretical model based on the stationary distribu- tion of bonus-malus classes on real-world data and a particular real bonus-malus system used in the Czech Republic. The empirical part of this thesis compares the optimal and the real relativities and assesses the suitability of the chosen theoretical model for the particular bonus-malus system. Keywords: bonus-malus system, a priori segmentation, stationary distribution, relativity, quadratic loss function 1
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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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Value of nonlife insurance portfolio
Pavko, Marek ; Koudelka, Pavel (advisor) ; Mazurová, Lucie (referee)
Název práce: Cena kmene neživotního pojištění Autor: Bc. Marek Pavko Katedra: Katedra pravděpodobnosti a matematické statistky Vedoucí diplomové práce: Mgr. Pavel Koudelka, Generali Pojiš'ovna a.s. Abstrakt: V práci se věnujeme r·zným přístup·m k ocenění portfólia neživotního pojištění. Podrobněji rozebíráme návrh modelu, který zkoumá hodnotu aktuálního obchodu pojiš'ovny. Odděleně se zaměřujeme na hodnotu obchodu pocházejícího z nadbytku rezerv na jedné straně a zvláš' analyzujeme hodnotu obchodu pocházejí- cího z obnovených smluv na straně druhé. V teoretické části návrhu se zaobíráme simulační metodou bootstrap, kterou využijeme k analýze rizika škodních rezerv. Navržený model aplikujeme na reálná data, která odpovídají odvětví neživotního pojištění. V závěru práce zkoumáme citlivost hodnoty aktuálního obchodu vzhledem ke změně jednotlivých parametr· navrženého modelu a diskutujeme možnost jejich ovlivnění z pohledu pojiš'ovny. Klíčová slova: ocenění portfólia, hodnota aktuálního obchodu, bootstrap, neživotní pojištění, Solvency II 1
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Multivariate extreme value theory
Šiklová, Renata ; Mazurová, Lucie (advisor) ; Omelka, Marek (referee)
In this thesis we will elaborate on multivariate extreme value modelling, re- lated practical and theoretical aspects. We will mainly focus on the dependence models, the extreme value copulas in particular. Extreme value copulas effec- tively unify the univariate extreme value theory and the copula framework itself in a single view. We familiarize ourselves with both of them in the first two chapters. Those chapters present generalized extreme value distribution, gen- eralized Pareto distribution and Archimedean copulas, that are suitable for the multivariate maxima and the threshold exceedances description. These two top- ics will be addressed in the third chapter in detail. Taking into consideration rather practical focus of this thesis, we examine the methods of data analysis extensively. Furthermore, we will employ these methods in a comprehensive case study, that will aim to reveal the importance of extreme value theory application in the Catastrophe Insurance. 1
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Lapse Analysis of Insurance Contracts
Strnad, Jan ; Mertl, Jakub (advisor) ; Mazurová, Lucie (referee)
The aim of the present work is to develop a tool for identification of Motor Third Party Liability insurance contracts which are at risk of cancellation. Methods for explorative data analysis, building a logistic regression model, comparing models and their validation and calibration are presented. Several models are developed on the real dataset using mentioned methods and then the final one is chosen. Behavior of the final model is verified by the validation on the out-of-time sample. Last step is calibration of the model to the expected value of the future portfolio cancellation rate.
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