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Modelování velkých škod
Petrová, Barbora ; Pešta, Michal (advisor)
Title: Large claims modeling Author: Barbora Zuzáková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta, Ph.D. Abstract: This thesis discusses a statistical modeling approach based on the extreme value theory to describe the behaviour of large claims of an insurance portfolio. We focus on threshold models which analyze exceedances of a high threshold. This approach has gained in popularity in recent years, as compared with the much older methods based directly on the extreme value distributions. The method is illustated using the group medical claims database recorded over the periods 1997, 1998 and 1999 maintained by the Society of Actuaries. We aim to demonstrate that the proposed model outperforms classical parametric distri- butions and thus enables to estimate high quantiles or the probable maximum loss more precisely. Keywords: threshold models, generalized Pareto distribution, large claims. 1
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Multivariate stochastic dominance and its application in portfolio optimization problems
Petrová, Barbora ; Kopa, Miloš (advisor) ; Ortobelli, Sergio (referee) ; Branda, Martin (referee)
Title: Multivariate stochastic dominance and its application in portfolio optimization Problems Author: Barbora Petrová Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D., Department of Probability and Mathematical Statistics Abstract: This thesis discusses the concept of multivariate stochastic dominance, which serves as a tool for ordering random vectors, and its possible usage in dynamic portfolio optimization problems. We strictly focus on different types of the first-order multivariate stochastic dominance for which we describe their generators in the sense of von Neumann-Morgenstern utility functions. The first one, called strong multivariate stochastic dominance, is generated by all nondecreasing multivariate utility functions. The second one, called weak multivariate stochastic dominance, is defined by relation between survival functions, and the last one, called the first-order linear multivariate stochastic dominance, applies the first-order univariate stochastic dominance notion to linear combinations of marginals. We focus on the main characteristics of these types of stochastic dominance, their relationships as well as their relation to the cumulative and marginal distribution functions of considered random vectors. Formulated...
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Comonotonic risks in financial and insurance applications
Palko, Maximilián ; Mazurová, Lucie (advisor) ; Petrová, Barbora (referee)
In actuarial mathematics we are often interested in distribution of a random vector. Sometimes these distributions might be too complicated. In this thesis we are going to study how to find an approximation of the random vector for which the distribution would be easier to obtain. Especially we will look for approxima- tions of sums of random variables. We will find out how this problem could be solved with knowledge of a dependency structure known as comonotonocity. For approximation of the random vector we will take his comonotonic counterpart. That would be more risky way but with knowledge of the dependency structure of the comonotonic random vector we will be able to obtain its distribution. In the last part of this thesis we will illustrate the use of findings about comonotonocity on examples. 1
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Basic approaches to robust conditional value at risk
Nožička, Michal ; Branda, Martin (advisor) ; Petrová, Barbora (referee)
The work describes conditional value at risk, its robustification with respect to the probability distribution of yields of assets and its applications to optimal portfolio selection. In chapter one there are definitions of conditional value at risk and its generalization throught robustification and also motivation to these definitions. The basic properties of conditional value at risk, mainly coherence and continuity with respect to the parametr of confidence level, are discussed in chapter two. There is also shown that some of these properties are preserved after robustification. The third chapter is dedicated to the derivation of optimization problems of optimal portfolio selection on the basis of conditional value at risk and its robustification. This thesis describes only special cases so that the final problems are solveble by the means of linear programming. The fourth chapter describes particular utilization of these methods with usage of real data from financial markets. Powered by TCPDF (www.tcpdf.org)
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Modelování velkých škod
Petrová, Barbora ; Pešta, Michal (advisor)
Title: Large claims modeling Author: Barbora Zuzáková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta, Ph.D. Abstract: This thesis discusses a statistical modeling approach based on the extreme value theory to describe the behaviour of large claims of an insurance portfolio. We focus on threshold models which analyze exceedances of a high threshold. This approach has gained in popularity in recent years, as compared with the much older methods based directly on the extreme value distributions. The method is illustated using the group medical claims database recorded over the periods 1997, 1998 and 1999 maintained by the Society of Actuaries. We aim to demonstrate that the proposed model outperforms classical parametric distri- butions and thus enables to estimate high quantiles or the probable maximum loss more precisely. Keywords: threshold models, generalized Pareto distribution, large claims. 1
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Regional differentiation in the EU
Petrová, Barbora ; Abrhám, Josef (advisor) ; Jelínek, Tomáš (referee)
The aim of the thesis is the regional differentiation analysis in the European Union territory. Thesis is focused on the EU Regional policy (its origin, development, objectives and instruments) and mainly on the demographic and economic differentiation in the EU. The demographic differentiation is qualified through the use of natural population increase, net migration and settlement structure. For the economic differentiation there have been used indicators such as GDP per inhabitant, employment and unemployment rate.
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CRM tools in banks
Petrová, Barbora ; Král, Petr (advisor) ; Pánek, Michal (referee)
Annotation This thesis is concerned with CRM approach - Customer relationship management. CRM covered new marketing methods, that are focused on client's needs rather than on product push strategy. Thanks to sophisticated data analysis clients are addressed with offers, that come up to their current needs. Thesis explains basic terms connected to CRM strategy, different sorts and its components. CRM concept is apllied on the banking area using the example of czech commercial bank.
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Oceňování nemovitostí
Petrová, Barbora ; Heřman, Jan (advisor) ; Hezina, Miloslav (referee)
Teoreticko-metodologická část práce je zaměřena na vysvětlení základních pojmů z oblasti oceňování. Dále se tato práce zabývá konkrétními pojmy, metodami a také riziky, která souvisejí s oceňováním nemovitostí. V praktické části je provedeno ocenění bytové jednotky administrativním způsobem dle cenového předpisu a také odhad její tržní hodnoty. V závěru je uvedeno porovnání zjištěných výsledků a posouzení jejich odlišnosti.
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