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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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Non-life Underwriting Risk in Solvency II - Undertaking Specific Parameters
Šimková, Barbora ; Justová, Iva (advisor) ; Mazurová, Lucie (referee)
of the bachelor's thesis Title: Non-life Underwriting Risk in Solvency II - Undertaking Specific Parameters Author: Barbora Šimková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Iva Justová Ph.D. Abstract: The thesis deals with methods by which it is possible to calculate specific estimate of standard deviation of risk in non-life premium risk. Premium risk is the risk caused by lack of insurance, when the undertaking does not have sufficient cover for future losses. Calculation methods are based on static methods and they comprise the knowledge taught at MFF UK. The thesis analyzes methods of calculating specific parameters and it explains how to calculate capital requirement for non-life premium and reserve risk; capital requirement reflects parameters of risk. An assessment of cap- ital requirements that uses specific parameters for an undertaking is in conclusion of the thesis. The evaluation is performed on a group of insurance companies from dif- ferent countries that used replacement of specific parameters in the calculation of risk premiums in Solvency II. Keywords: non-life underwriting risk, Solvency II, undertaking specific parameters
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Solvency II Methods for Life Insurance
Benešová, Martina ; Finfrle, Pavel (advisor) ; Mazurová, Lucie (referee)
Název práce: Metodiky Solvency II v životním pojištění Autor: Martina Benešová Katedra (ústav): Katedra pravděpodobnosti a matematické statistiky Vedoucí bakalářské práce: RNDr. Pavel Finfrle, Ph.D e-mail vedoucího: finfrle@generalippf.eu Abstrakt: Tato diplomová práce se zabývá problematikou solventnosti pojišťoven v souvislosti s konceptem regulatorního rámce Solvency II. Na začátku práce jsou shrnuté základní body o Solvency I, dále je větší pozornost věnovaná vlastnostem Solvency II a jednotlivým kategoriím rizik, jejichž správná kvantifikace je pro Solvency II klíčová. V další části jsou představeny metody na výpočet kapitálové dostatečnosti - interní a částečné interní modely a podrobněji pak standardní model. Klíčové dvě kapitoly práce se pak detailně zabývají rizikem storen v ži- votním pojištění. Rozebrána je standardní metodika výpočtu kapitálového poža- davku, a je navržen stochastický model, který ji rozšiřuje zahrnutím informace o diverzitě odbytových cest. Monte Carlo simulací je demonstrována nižší rizikovost pojišťovny s širším polem zprostředkovatelů. Klíčová slova: solventnost, Solvency II, kapitálové požadavky, riziko storen Title: The methods of Solvency II for life insurance Author: Martina Benešová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Pavel...
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Výpočet rizikového kapitálu pro investiční životní pojištění
Coufal, Tomáš ; Lukášek, Josef (advisor) ; Mazurová, Lucie (referee)
Title: Risk capital calculation in invesment life insurance Author: Bc. Tomáš Coufal Department/Institute: Department of Probability and Mathematical Statis- tics Supervisor of the master thesis: Mgr. Josef Lukášek Supervisor's e-mail address: Josef.Lukasek@allianz.cz Abstract: Unit linked insurance is a modern and flexible life insurance product. The last decade was marked by the raising popularity of unit linked insurance. The discussions conserning the impact of the new directive Sol- vency II on the life insurance business focus mainly on the traditional life insurance. This paper examines the issue of the calculation of the risk capital for unit linked insurance. Analysis of the impact of different death guaran- tees, forms of premium payment, time to maturity and dynamic policyholder bahaviour on the risk capital is presented. Keywords: Unit linked insurance, Solvency II, Risk capital, Solvency capital requirement
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Zpětná alokace diversifikačního efektu v pojistném riziku
Kyseľová, Soňa ; Středová, Marcela (advisor) ; Mazurová, Lucie (referee)
The determination of the sufficient amount of economic capital and its allocation to the business lines is the key issue for insurance companies. In this thesis we introduce two methods of aggregating economic capital. One is based on linear correlation and the second deals with copulas. A multitude of allocation principles have been proposed in the literature. We choose those which are the most used in practice and compare advantages and disadvantages of their application. The last chapter is devoted to the numerical examples of capital aggregation and allocation principles. 1
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Longevity Risk in Life Insurance
Danešová, Zdenka ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
In this thesis we deal with the longevity risk originating from the uncertain future evolution of mortality at adult-old ages. It may emerge in particular because of an unanticipated reduction in mortality rates. That risk is significant for annuity and pension providers. We consider a model portfolio represented by one cohort of recipients of immediate life annuities. We introduce possibilities for assessing the risk of such portfolio. A comparison of the impact of longevity risk is made with random deviations in mortality rates. We also deal with the question of solvency of the insurer by investigating the solvency capital requirement for longevity risk.
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