The diploma thesis covers a design and an assesment of a timber bearing structure of sports hall. The plan of the hall is round, i.e. the object is shaped as a dome. The structure is designed in two ways: geodesic and ribbed dome. Both options are made of glued laminated timber and structural timber.

The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.

The dependence structures in financial markets count among the most frequently discussed topics in the recent literature. However, no general consensus on modeling of the cross-market linkages has been reached. This thesis analyses the dependence structure and contagion in the financial markets in Central and Eastern Europe. Tail dependence, symmetry and dynamics of the dependence structure are examined. A conditional copula framework extended by recently developed dynamic generalized autoregressive score (GAS) model is used to capture the conditional time-varying joint distribution of stock market returns. Considering the Czech, Croatian, Hungarian, Austrian and Polish stock market indices over the 2005-2012 period, we find that time-varying Student's t GAS copula provides the best fit. The results show, that the degree of dependence increases substantially during the global financial crisis, having a direct impact on portfolio optimization.

Diploma thesis abstract Thesis title: Statistical inference in multivariate distributions based on copula models Author: Vojtěch Kika This diploma thesis aims for statistical inference in copula based models. Ba- sics of copula theory are described, followed by methods for statistical inference. These are divided into three main groups. First of them are parametric methods for copula parameter estimation which assume fully parametric structure, thus for both joint and marginal distributions. The second group consists of semi- parametric methods for copula parameter estimation which, unlike parametric methods, do not require parametric structure for marginal distributions. The last group describes goodness-of-fit tests used for testing the hypothesis that consi- dered copula belongs to some specific copula family. The thesis is accompanied by a simulation study that investigates the dependence of the observed coverage of the asymptotic confidence intervals for copula parameter on the sample size. Pseudolikelihood method was chosen for the simulation study since it is one of the most popular semiparametric methods. It is shown that sample size of 50 seems to be sufficient for the observed coverage to be close to the theoretical one. For Frank and Gumbel-Hougaard copula families even sample size of 30 gives us...

Some methods for generating scenarios from multidimensional distribution assume we are able to generate scenarios from the one-dimensional distribution. We dedicate chapter 3 to this problem. At the end of the chapter, we provide references for applicable algorithms. Chapter 4 is focused on selected methods for generating scenarios from multidimensional distributions. In chapter 4.3, we introduce an algorithm for generating scenarios, which do not use any assumption about the distribution, except the first four moments and correlations to be specified. A method of generating scenarios based on approximation of multivariate normal distribution by the binomial distribution is described in chapter 4.5. Dimension reduction technique using principal components is presented in chapter 4.4. The algorithm is presented under the assumption of normal distribution. In chapter 4.6, we introduce the basics of the copula theory and a method for generating scenarios by C-vine copula. In chapter 5, we implement selected methods for generating scenarios for the estimation of daily value at risk for selected indexes and we discuss the results. Powered by TCPDF (www.tcpdf.org)

Title: A study of applying copulas in data mining Author: Martin Ščavnický Department: Department of Theoretical Computer Science and Mathe- matical Logic Supervisor: RNDr. Ing. Martin Holeňa CSc., Department of Theoretical Computer Science and Mathematical Logic Abstract: Copulas are functions that describe the relationship between a multivariate distribution function and its marginals. They provide a way to model multivariate distribution functions, and are extensively used in finance and studied in data mining. In practice, there are many different copula families and no standard way for choosing the right one. In our work, we compare suitability of different copula families in data mining. We fit classification data using 8 copula families and compare them using 3 mea- sures of fit. We also use a classification algorithm based on copulas and compare its accuracy for different copula families. The results indicate that elliptical copulas fit our data better, but hierarchical Archimedean copulas give comparable accuracy in the classification. We also propose and test a modified method for modelling data using hierarchical Archimedean copu- las, which fits some datasets with negative dependence between attributes better. Based on this modified method, we propose a visualization of depen- dence in data and observe...

Multidimensional frequency models can be used for modeling number of claims from different branches which are somehow dependent on each other. As in the one-dimensional case Poisson distribution and negative binomial distribution are primarily used for modeling multidimensional claim counts data, only they are extended to higher dimensions. The generalization of multi- dimensional distributions is often done using so-called shock variables, where one random variable is included in all dimensions of a random vector which models claim counts. The more comprehensive approach to modeling dependence uses copulas. Comparison of these models is done on a simulated data of number of claims from two different car insurance guarantees.

Model-based black-box optimization is a topic that has been intensively studied both in academia and industry. Especially real-world optimization tasks are often characterized by expensive or time-demanding objective functions for which statistical models can save resources or speed-up the optimization. Each of three parts of the thesis concerns one such model: first, copulas are used instead of a graphical model in estimation of distribution algorithms, second, RBF networks serve as surrogate models in mixed-variable genetic algorithms, and third, Gaussian processes are employed in Bayesian optimization algorithms as a sampling model and in the Covariance matrix adaptation Evolutionary strategy (CMA-ES) as a surrogate model. The last combination, described in the core part of the thesis, resulted in the Doubly trained surrogate CMA-ES (DTS-CMA-ES). This algorithm uses the uncertainty prediction of a Gaussian process for selecting only a part of the CMA-ES population for evaluation with the expensive objective function while the mean prediction is used for the rest. The DTS-CMA-ES improves upon the state-of-the-art surrogate continuous optimizers in several benchmark tests.

The Master´s thesis contains design of steel construction of exhibition pavilion, which is consists of columns, dome, lantern and suspension footbridge. Building will be intended for organizing exhibitions and conferences by town Trutnov. Two models of variants of dome´s construction are drafted in this work– Schwedler´s and Föpple´s dome. Models are space tubular structures.The work contains static assessment of spatial structures and spherical steel joint in program SCIA Engineer for both variants. Hand assessment of bars, basic details and anchoring, technical report and drawing dokumentation are drafted for selected variant construction with Schwedler´s dome.

In the present work we study the securitized products of ?financial markets with focus on collateralized debt obligations and the impact of fi?nancial crisis on the markets in the world. First part the thesis is focused on the methodology of the reasons behind launching these products, the portfolio, tranches and further on mechanisms how these structures are working. In the second part the thesis teoretically describes the valuation methods for which the Markov chains and copula functions are used. Further on follows the practical part with output from the quantitative analysis and at the end the thesis describes the impacts on economics of di?fferent countries and practically introduces the stress testing as the precaution tool.