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Financial risks with copulas
Prelecová, Natália ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
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.
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Model-based evolutionary optimization methods
Bajer, Lukáš ; Holeňa, Martin (advisor) ; Brockhoff, Dimo (referee) ; Pošík, Petr (referee)
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.
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The experimental family house
Švorcová, Barbora ; Buchta, Stanislav (referee) ; Šmak, Milan (advisor)
The subject of the bachelor thesis is the design of an experimental residential house. The proposed structure has the form of a free-standing dome, which covers a building located inside. The area around the building under the dome creates space for an unconventional winter garden. The construction of the roof was designed and assessed in terms of geometry in two variants, in the shape of a geodesic and ribbed dome, with diameter 24 m and height 12 m. The considered material of the ribbed dome is glued laminated timber. In addition to the wooden one, the geodesic dome was also designed in a steel variant. Within the bachelor‘s thesis, the structural load, limit states and design of the main joints were dealt with. The house under the dome was considered in the form of a study of possible designs. In addition to the traditional light-frame construction, a structure made of panels of cross-laminated timber was also assessed.
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Cyber risk modelling using copulas
Spišiak, Michal ; Teplý, Petr (advisor) ; Baruník, Jozef (referee)
Cyber risk or data breach risk can be estimated similarly as other types of operational risk. First we identify problems of cyber risk models in existing literature. A large dataset consisting of 5,713 loss events enables us to apply extreme value theory. We adopt goodness of fit tests adjusted for distribution functions with estimated parameters. These tests are often overlooked in the literature even though they are essential for correct results. We model aggregate losses in three different industries separately and then we combine them using a copula. A t-test reveals that potential one-year global losses due to data breach risk are larger than the GDP of the Czech Republic. Moreover, one-year global cyber risk measured with a 99% CVaR amounts to 2.5% of the global GDP. Unlike others we compare risk measures with other quantities which allows wider audience to understand the magnitude of the cyber risk. An estimate of global data breach risk is a useful indicator not only for insurers, but also for any organization processing sensitive data.
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The botanical pavillion in Jihlava
Kuchtová, Ludmila ; Buchta, Stanislav (referee) ; Šmak, Milan (advisor)
The aim of this diploma thesis is to design a load-bearing structure of the botanical pavillion in Jihlava. The construction is designed as a variable structure of both steel and timber. Each solution has a different type of ribs. The layout is a hexadecagon with maximum dimension of 30 meters. The height of the building is considered to be 10 meters.
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Multivariate claim numbers models
Zušťáková, Lucie ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
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.
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Glasshouse
Sejbalová, Kateřina ; Šmak, Milan (referee) ; Barnat, Jan (advisor)
This master thesis deals with design of a load-bearing steel structure, i tis located in ZOO Zlín areal. The building serves as a glasshouse. It is a single-storey building with circle plan, 39,04 m diameter and 15,63 m height. Space construction follows spherical cap of a sphere with diameter 40 m. Variant A building is design as a fuller dome. Variant B building consists of hexagons, which are getting smaller with height, at the upper part is the hexagonal geometry cancelled and geometry made from triangles follows. This thesis contains design of a pedestrian bridge, which carries all technical loads. The thesis contains static report of the beams a design of main joints.
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Hangar
Matějková, Pavla ; Štrba, Michal (referee) ; Barnat, Jan (advisor)
Diploma thesis contains a design of steel load-bearing structure of a hangar placed in Brno-Medlánky. The ground dimensions are 40.0×44.0 m, the height of the building is 10.0 m. Two preliminary variants of the design solution were processed; main difference is the shape of the truss girder. Both variants were assessed for a combination of seventeen load cases. The comparison of the variants led to the selection of the final variant, which was assessed in detail. The girder truss in this variant is an arched truss, the height of the truss is 1.5 m, the individual elements are made of square hollow sections. A detailed static calculation was performed including the calculation of joints, drawing documentation and technical report. The main construction material is S235JR steel.
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Model-based evolutionary optimization methods
Bajer, Lukáš ; Holeňa, Martin (advisor) ; Brockhoff, Dimo (referee) ; Pošík, Petr (referee)
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.
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Statistical inference in multivariate distributions based on copula models
Kika, Vojtěch ; Omelka, Marek (advisor) ; Hlubinka, Daniel (referee)
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...
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