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Superposition and thinning of counting processes in non-life insurance
Romaňák, Martin ; Pešta, Michal (advisor) ; Kříž, Pavel (referee)
The thesis examines a model for representing the number of claims after merging or splitting different lines of business of an insurance company. The model is based on count- ing processes, the Poisson and the renewal processes are considered in particular. The operations of superposition and thinning are the proposed solution to this problem. We present the well-known results that the Poisson processes are closed under superposition and several types of thinning and explore the necessary conditions for this statement to also hold for renewal processes. Specifically, the previous work on the superposition of renewal processes is studied and further clarified, and an original result is derived for two types of thinning of a renewal process. The theoretical results are then used to analyze real insurance data in a model situation when an insurance company wants to estimate the future number of claims after merging two of its lines of business. 1
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Two-dimensional distributions for given margins
Šťastný, Filip ; Pešta, Michal (advisor) ; Omelka, Marek (referee)
One of the tools for study of dependence between random variables are co- pulas. While modelling multidimensional variables it is possible using Sklar's theorem to model through copulas marginal distributions and relationship be- tween them separately, this approach thus enables us to split construction of multi-dimensional distributions into these two factors. With marginal distributi- ons fixed, the construction is consisting of appropriate copula choice only. This thesis deals with copulas in the case of two-dimensional distributions with conti- nuous fixed marginal distributions and is focused on parametrical copulas, mainly through Archimedean copulas. Basic properties of copulas with Sklar's theorem, which enables studying copulas in stochastic context, are presented here. Further, measures of dependence such as Kendall's tau, Spearman's rho and coeficients of tail dependence are in connection with copulas studied in this thesis. At the end, the thesis deals with methods of estimation unknown parameters, which are ilustrated on two examples. 1
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Czechoslovak-Libyan Cooperation in Health Care
Fischer, Philipp-Jakob ; Vojtěchovský, Ondřej (advisor) ; Pešta, Mikuláš (referee)
The thesis is focused on Czechoslovak-Libyan contacts in the healthcare sector from approximately the seventies to 1989. The pivotal period was the healthcare cooperation taking place in the eighties. The focus of this cooperation was primarily Czechoslovak medical experts who worked in Libyan medical institutions. The purpose of the work is to reveal the political and historical background of cooperation. Find out why it happened, how it happened and what it was about. The text also deals with the importance of cooperation for Czechoslovakia and Libya. Last but not least, the author tries to uncover the forgotten life stories of Czechoslovak medical professionals. It pays attention to their role in the cooperation, their motivation to travel to Libya and reconstructs the process of preparation, deployment and life in Libya. It also tracks the chronological development of the number of Czechoslovak medical professionals in Libya. The work highlights the efforts of these experts who have really helped thousands of Libyans and contributed to the development of the Libyan healthcare system. The text is the result of an extensive analysis of archival sources.
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"From a Left-Wing Intellectual to a pro-American Liberal?" The Development of President Vaclav Havel's Thought in Relation to the USA and NATO
Libnar, Vojtěch ; Pešta, Mikuláš (advisor) ; Johnston, Rosamund (referee)
The diploma thesis deals with selected views of Václav Havel after 1989, taking into account his previous ideas. It traces the development of Václav Havel's attitudes towards the North Atlantic Alliance, the contemplated, prepared and finally realized membership of the Czech Republic in this organization. Furthermore, the thesis examines Havel's personal ties to selected American officials and reflects on their views of Václav Havel. These include Presidents George H. W. Bush, Bill Clinton, George W. Bush, and Secretary of State Madeleine Albright. The thesis then turns in the final section to Havel's views on selected military interventions that were directly led by, or in which the United States was the major force - the Gulf War, the bombing of Yugoslavia, and the invasion of Iraq. Through these perspectives, it seeks to answer the question of whether Havel's worldview changed fundamentally during his presidency, and whether Havel uncritically embraced support for American foreign policy. Whether Havel had turned from a rather left-leaning intellectual from dissident circles into a Central European post-Communist statesman who was absorbed by the triumphalist atmosphere of the 1990s and his admiration for the United States. Or whether Havel has partly maintained his critical distance and lived...
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Bagging and regression trees in individual claims reserving
Janoušek, Jan ; Pešta, Michal (advisor) ; Mizera, Ivan (referee)
This diploma thesis focuses on the application of classification and regression trees, as well as bootstrap aggregating, to individual reserving in insurance. In the first part, we provide a summary of the theory and establish mathematical formalities that are sometimes overlooked in basic texts on these topics. We provide a comprehensive overview of the concepts, including a detailed discussion of their practical applications. In the second part, we build on existing research by extending the use of machine learning in individual claims reserving. Specifically, we expand on a prior article that only modeled the number of claims using classification trees. We also incorporate regression trees and bagging to model the size of each claim, resulting in more accurate reserve estimates. We achieve this by applying these techniques to insurance data and obtaining empirical distributions that allow us to calculate confidence intervals and quantiles. Ultimately, we determine the reserves needed for both the next year and the ultimate reserves. 1
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Hydrogel Scaffolds for Tissue Engineering
Chocholatá, Petra ; Babuška, Václav (advisor) ; Kovařík, Tomáš (referee) ; Pešta, Martin (referee)
Bone tissue engineering attempts to mimic the natural behavior of hard connective tissues. Currently, there is an active research and development of new functional materials in this field. The main direction in the treatment of bone tissue defects is the use of biodegradable composite materials based on biopolymers enriched with an inorganic component, possibly in combination with a cellular component. In general, hydrogels play an important role in tissue engineering due to their properties, as they can respond relatively well to changes in environmental conditions and are used as a suitable medium for cells to grow and proliferate. Structure of hydrogels also allows nutrients and waste products to diffuse, and the last but not least, thanks to this they can also serve as drug carries. A major advantage of hydrogels is that they can be injected with subsequent in situ gelation. In this work, physically cross-linked hydrogels based on polyvinyl alcohol (PVA) and hyaluronic acid (HA) in different volume ratios enriched with hydroxyapatite (HAp), an inorganic component inherent to bone tissue, were compared. Incorporation of HAp into the organic matrix was performed in two different ways, by in situ synthesis directly in the PVA/HA matrix and by physical mixing of pre-prepared HAp. The composition of...
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The First Decade of the Existence of the Federal Republic of Germany as Seen Through the Eyes of the Czechoslovak Military Mission to the Allied Control Council in Germany - The Development of the Problem from the Second World War to 1958
Fousek, Pavel ; Pešta, Mikuláš (advisor) ; Horčička, Václav (referee)
The period of more than ten years after the end of the Second World War is characterised by revolutionary changes that led to the emergence of new power formations. After the Second World War, the Cold War divided Europe and the world into two antagonistic camps - the West represented by the United States of America and the East led by the Soviet Union. The new balance of power also had a major impact on Czechoslovak-West German relations. The complexity of this relationship was due not only to the historical context itself, with its painful wartime experiences, but also to the fact that the Federal Republic of Germany had from the outset sought integration into Western structures, while the Czechoslovak Republic was transformed after February 1948 into part of the so-called Eastern bloc. The diploma thesis focuses on how the Czechoslovak Military Mission, which operated in West Berlin from the second half of the 1940s in the role of Czechoslovak diplomatic and consular representation, reflected Czechoslovak-West German relations. The aim of this thesis was to find out how this military mission interpreted the events in the Federal Republic of Germany in the period from 1949 to 1958 in terms of three key points - the issue of forcibly displaced people, especially the so-called Sudeten Germans, the...
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Chain-ladder method as maximum likelihood estimator in Poisson model
Wagner, Vojtěch ; Kříž, Pavel (advisor) ; Pešta, Michal (referee)
First, the distribution-free chain-ladder is introduced. Then, the Poisson model is in- troduced. It is proven that the total reserves for one accident year given by the maximum likelihood estimation applied to the Poisson model lead to the identical reserves as the reserves derived from the distribution-free chain-ladder used in the Poisson model. Later, inadequacies of the Poisson model are discussed. Hessian matrices of the log-likelihood evaluated at the Poisson estimators are analyzed. The question whether the inverse of the Fisher information matrix approximates the real covariance matrix of the Poisson esti- mators is explored. Comparing the variance of the total reserves derived from the inverse of the Fisher information and the real covariance matrix leads to negative conclusion, that the former does not approximate the latter well. 1
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Czechoslovak Development Aid to the Algerian People's and Democratic Republic in the Years 1962-1965
Kopenec, Karel ; Pešta, Mikuláš (advisor) ; Mazanec, Jakub (referee)
Algeria gained its independence on March 19, 1962, after signing the Evian Accords with France. The accords ended Algeria's eight-year war of independence. Czechoslovakia already supported the Algerian side during the war, mainly by exporting arms. On the part of Czechoslovakia, it was primarily a business partnership and support of a potential ally during the Cold War. However, the Communist Party of Algeria came out of the war as a loser, its influence on events in the new state was minimal. In Algeria, the National Liberation Front came to power. This fact, however, did not prevent communist Czechoslovakia from providing further support to the newly formed state. Foreign aid was needed for Algeria, the war destroyed the already existing infrastructure, and moreover, the absence of French experts was noticeable for the country's economy. The thesis deals with the level of Czechoslovak development aid to Algeria in the first years of its independent existence and answers the following questions. For what purpose was aid provided by the Czechoslovakia to the newly emerging state of Algeria? Were these goals that the Czechoslovak Republic set for itself when establishing new relations with Algeria achieved? To which areas was Czechoslovak aid primarily directed? At the beginning, the thesis deals...
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