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Title: Parameterization of claims distribution in non-life insurance Author: Bc. Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta Ph.D., MFF UK Abstract: This paper deals with the parameterization of claim size distributions in non-life insurance. It consists of the theoretical and the practical part. In the first part we discuss the usual distributions of claims and their properties. One section is devoted to extreme values distributions. Consequently, we mention the most known methods for parameter estimation - the maximum likelihood method, the method of moments and the method of weighted moments. The last theoretical chapter is focused on some validation techniques and goodness-of-fit tests. In the practical part we apply some of the discussed approaches on real data. However, we concentrate mainly on the large claims modeling - firstly, we select a reasonable threshold for our data and then we fit the claims by the generalized Pareto distribution together with the introduced parameterization procedures. Based on the results of the applied validation methods we will choose appropriate models for the biggest claims. Keywords: parameterization, non-life insurance, claims distribution.

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.

Práce podrobně analyzuje tendence ve vývoji produktové stuktury na českém pojistném trhu. Podrobně se zaměřuje na zachycení změn a jejich přičin ve struktuře pojistných produktů v posledním období. Snahou bylo uvést důležité aspekty vedoucí k přizpůsobování se produktové struktury tržnímu hospodářství. Zmíním produkty nacházející se v současné době na českém pojistném trhu na konkrétních číslech a demonstruji jejich vývoj v posledních letech. Srovnám životní a neživotní pojištění. Prognózování možného a předpokládaného složení struktury obou segmentů do budoucích let nejenom v návaznosti vstupu České republiky do Evropské unie je konečným cílem práce.

Title: Solvency Internal models Author: Mgr. Ing. Jakub Mertl Abstract: The subject of thesis is assessment of calculation methods on capital adequacy of currently implemented regulation in insurance industry called Solvency II. The aim of the thesis is to build up a partial internal model fulfilling the condition of Solvency II. The thesis deals with the premium and reserve risks that are essential part of non-life business. Different approaches of risk assessment are described and aggregation of those risks as well. An important part of the thesis is a numerical example illustrating presented methods.

i Abstract: This thesis assesses the impact of economic, institutional and demographic factors on the life and non-life gross written premiums of insurance companies. A dynamic panel data regression using the system generalized method of mo- ments is applied on data of 29 European countries collected by EIOPA covering the period from 2005 to 2013. The results reveal that economic and institutio- nal factors drive both life and non-life insurance industry. On the other hand, we cannot confirm that demographic factors are significant determinants of the growth in GWPs. Subsequently, the hypothesis that there are substantial cross-countries differences among the importance of different macroeconomic determinants on the insurance sector development is explored and confirmed. This work shines new light on the development of the quantitative macro- prudential framework used to determine different economic scenarios affecting insurance companies' balance sheets. Moreover, a broader set of panel data and more variables explaining the growth in insurance sector bring new contributi- ons to the current discussion in academic literature.

This thesis deals with analysis of development in insurance penetration of the Czech republic. The importance of insurance is growing in years, what is numerically expressed in values of insurance penetration indicators. This thesis is focused on development in the Czech republic between years 2000-2010. To review values in the broader context will be indicators compared with EU countries. The thesis is finished by summary of the insurance penetration in the Czech republic and by the prognosis of the further development.

The thesis analyses recent important issues affecting the insurance industry (both global and local). 1.EU anti-discrimination policy's impact on insurance risk 2.Catastrophe Risks and Reinsurance, Earthquake in Japan, 2011 3.BankInsurance - Single-Premium Life Insurance 4.Pension reform: New opportunities for private insurers 5.The reasons of low performance of non-life insurance industry

The diploma thesis introduces the issue of insurance frauds from the perspective of the Czech and Slovak Republic. An essential part is characteristic of insurance markets of both countries and their specific definitions and their continuities. The elementary terminology in context with the topic is demarcated and attention is paid to the legislation of both countries, with particular emphasis on the Criminal Codes, which classify insurance fraud as an the object of financial crime. The main part of this thesis consists in the construction of regression models and the use of correlation analysis and time series analysis to detect the relationships and the degree of impact of selected indicators on the trend of proven insurance frauds. The expected developments in the near future are formulated and identified trends in the insurance frauds in both countries are faced to mutual comparison.