Das vorliegende Skript ist aus einer Lehrveranstaltung hervorgegangen, die von mir mehrere Jahre an der Fakultät Wirtschaftswissenschaften der TU Dresden gehalten wurde. Diese Lehrveranstaltung hatte erst die Bezeichnung "Monetäre Risikomaße" und später "Risikomaße". Mehrere frühere Fassungen dieses Skripts, das häufig überarbeitet und erweitert wurde, trugen den Namen Monetäre Risikomaße (Auflagen 1 bis 7). Die einzelnen Kapitel enthalten in der Regel die drei abschließenden Abschnitte "Übungsaufgaben", "Beweise" und "Ergänzung und Vertiefung" mit Material zum jeweiligen Kapitel, das nicht in der Vorlesung vorgetragen wurde.

>Magister Scientiae - MSc / The case of pricing options under constant volatility has been common practise for decades. Yet market data proves that the volatility is a stochastic phenomenon, this is evident in longer duration instruments in which the volatility of underlying asset is dynamic and unpredictable. The methods of valuing options under stochastic volatility that have been extensively published focus mainly on stock markets and on options written on a single reference asset. This work probes the effect of valuing European call option written on a basket of currencies, under constant volatility and under stochastic volatility models. We apply a family of the stochastic models to investigate the relative performance of option prices. For the valuation of option under constant volatility, we derive a closed form analytic solution which relaxes some of the assumptions in the Black-Scholes model. The problem of two-dimensional random diffusion of exchange rates and volatilities is treated with present value scheme, mean reversion and non-mean reversion stochastic volatility models. A multi-factor Gaussian distribution function is applied on lognormal asset dynamics sampled from a normal distribution which we generate by the Box-Muller method and make inter dependent by Cholesky factor matrix decomposition. Furthermore, a Monte Carlo simulation method is adopted to approximate a general form of numeric solution The historic data considered dates from 31 December 1997 to 30 June 2008. The basket contains ZAR as base currency, USD, GBP, EUR and JPY are foreign currencies.

In alkalischen Lösungen führt die Reaktion von Hydroxylionen mit den Si-O-Si-Bindungen des Glasnetzwerks zur Bildung hydratisierter Oberflächen und gelöstem Silikat. Der Grad der Korrosion bzw. der Alterung der Glasfaser ist abhängig von der chemischen Zusammensetzung des Glases und Korrosionslösung sowie von Zeit und Temperatur. Die Untersuchung von Glasfasern verschiedener chemischer Zusammensetzung in NaOH- sowie Zementlösungen zeigte, dass die inhibierende Wirkung von Ca-Ionen zu einem veränderten Korrosionsmechanismus führt. Dies konnte anhand der mechanischen Eigenschaften der Glasfasern sowie rasterelektronenmikroskopischen Untersuchungen gezeigt werden. Während die Korrosion in NaOH-Lösung zu einer ausgeprägten Umwandlung der gesamten äußeren Glasfaserschicht in Reaktionsprodukte führte, zeigten Glasfasern in Zementlösung bei gleichem pH-Wert einen stark lokal begrenzten, punktförmigen Angriff. Daraus resultieren unterschiedliche mechanische Eigenschaften der Glasfasern in Abhängigkeit von der gewählten Korrosionslösung.

RCs (Reverberation Chambers) has historically been used mainly for aerospace and military purposes in EMC (Electromagnetic Compatibility) testing, but the interest also seems to increase in the automotive industry (the development of an international standard for vehicles is in progress). The vehicles of the future will most likely be electrified, wirelessly connected and autonomous, i.e., more control units, more communication systems, and more sensors, will be implemented in the vehicles requiring increased robustness against all possible electromagnetic interferences. EMC testing in an RC is a step in the direction of ensuring this robustness for the future vehicle platforms. Compared to a traditional EMC test method in a fully or semi-AC (Anechoic Chamber), testing in an RC has the advantage that the electromagnetic field will be isotropic, randomly polarized and homogeneous in a statistical sense, i.e., the exposed object will be surrounded by electromagnetic energy from all directions. It can be considered relatively expensive to build a brand new RC with motorized stirrers and associated measurement instrumentation, instead it would be desirable to perform immunity tests in a more cost-effective conductive fabric tent. The great advantage is the flexibility, the tent can be set up almost anywhere, even in already existing semi-ACs, such set-up is referred to as VIRC (Vibrating Intrinsic Reverberation Chamber). This thesis aims to develop a new test method in a VIRC environment. In order to achieve good RC conditions, the electromagnetic field must be statistically Rayleigh distributed. Furthermore, it is of great importance to avoid LoS (Line of Sight) between the antenna and the test object, and to achieve good stirring in the tent. Provided this can be achieved, there are still some challenges by testing in a tent. For example, the classical dwell time of two seconds for immunity testing in EMC is not possible to achieve in a VIRC environment. The validation in this thesis shows that the dwell time or the total exposure time in the tent might be enough to trigger possible malfunctions in today's modern high-speed communication vehicles. Furthermore, it is showed, testing in a VIRC gives good field uniformity and repeatability, and can trigger malfunctions that are not triggered in traditional EMC testing in semi-AC, i.e., ALSE (Absorber-Lined Shielded Enclosure) testing.

An in-depth knowledge of the structure formation process and the resulting dependency of the morphology on the reaction mechanism is a key requirement in order to design application-oriented materials. For twin polymerization, the basic idea of the reaction process is established, and important structural properties of the final nanoporous hybrid materials are known. However, the effects of changing the reaction mechanism parameters on the final morphology is still an open issue. In this work, the dependence of the morphology on the reaction mechanism is investigated based on a previously introduced lattice-based Monte Carlo method, the reactive bond fluctuation model. We analyze the effects of the model parameters, such as movability, attraction, or reaction probabilities on structural properties, like the specific surface area, the radial distribution function, the local porosity distribution, or the total fraction of percolating elements. From these examinations, we can identify key factors to adapt structural properties to fulfill desired requirements for possible applications. Hereby, we point out which implications theses parameter changes have on the underlying chemical structure.

In this thesis we present results about some eigenvalue statistics of the beta-Hermite ensembles, both in the classical cases corresponding to beta = 1, 2, 4, that is the Gaussian orthogonal ensemble (consisting of real symmetric matrices), the Gaussian unitary ensemble (consisting of complex Hermitian matrices) and the Gaussian symplectic ensembles (consisting of quaternionic self-dual matrices) respectively. We also look at the less explored general beta-Hermite ensembles (consisting of real tridiagonal symmetric matrices). Specifically we look at the empirical distribution function and two different scalings of the largest eigenvalue. The results we present relating to these statistics are the convergence of the empirical distribution function to the semicircle law, the convergence of the scaled largest eigenvalue to the Tracy-Widom distributions, and with a different scaling, the convergence of the largest eigenvalue to 1. We also use simulations to illustrate these results. For the Gaussian unitary ensemble, we present an expression for its level density. To aid in understanding the Gaussian symplectic ensemble we present properties of the eigenvalues of quaternionic matrices. Finally, we prove a theorem about the symmetry of the order statistic of the eigenvalues of the beta-Hermite ensembles. / I denna kandidatuppsats presenterar vi resultat om några olika egenvärdens-statistikor från beta-Hermite ensemblerna, först i de klassiska fallen då beta = 1, 2, 4, det vill säga den gaussiska ortogonala ensemblen (bestående av reella symmetriska matriser), den gaussiska unitära ensemblen (bestående av komplexa hermitiska matriser) och den gaussiska symplektiska ensemblen (bestående av kvaternioniska själv-duala matriser). Vi tittar även på de mindre undersökta generella beta-Hermite ensemblerna (bestående av reella symmetriska tridiagonala matriser). Specifikt tittar vi på den empiriska fördelningsfunktionen och två olika normeringar av det största egenvärdet. De resultat vi presenterar för dessa statistikor är den empiriska fördelningsfunktionens konvergens mot halvcirkel-fördelningen, det normerade största egenvärdets konvergens mot Tracy-Widom fördelningen, och, med en annan normering, största egenvärdets konvergens mot 1. Vi illustrerar även dessa resultat med hjälp av simuleringar. För den gaussiska unitära ensemblen presenterar vi ett uttryck för dess nivåtäthet. För att underlätta förståelsen av den gaussiska symplektiska ensemblen presenterar vi egenskaper hos egenvärdena av kvaternioniska matriser. Slutligen bevisar vi en sats om symmetrin hos ordningsstatistikan av egenvärdena av beta-Hermite ensemblerna.

The scientific work is related to the theoretical study of the structural properties of concentrated magnetic fluids. We must be a theoretical investigate of structural properties of magnetic fluid for the effective application and synthesis of magnetic fluid. This work is devoted to investigation of interparticle correlations in magnetic fluids, because the real magnetic fluids are polydisperse in their particle size distribution. magnetic fluids is modeled bidisperse system of hard spheres, in the absence of an external magnetic field. Analytical expressions are provided for the pair distribution function and structure factor . These functions make it possible to analyze the internal structure of ferrofluids. The developed theory is compared with the results of computer simulations conducted at the University of Edinburgh, to determine the scope of applicability of the theory. It is shown that the obtained analytical expressions can be successfully applied in a sufficiently wide range of concentrations with moderate ferroparticles interparticle dipole-dipole interaction. The typical behavior of the pair distribution function and structural factor are analyzed in dependence on the particle size distribution in the system. The analytically structure factor analytically is compared with experimental results. / Научная работа связана с теоретическим изучением структурных свойств концентрированных магнитных жидкостей. Для эффективного применения и синтеза магнитной жидкости необходимо теоретическое исследование ее структурных свойств. Поскольку реальные магнитные жидкости являются полидисперсными по своему гранулометрическому составу, данная работа посвящена исследованию межчастичных корреляций в магнитных жидкостях, которая моделируется бидисперсной системой твердых сфер, в отсутствие внешнего магнитного поля. Определено аналитическое выражение для парной функции распределения и структурного фактора рассеяния. Эти функции дают возможность проанализировать внутреннюю структуру феррожидкостей. Построенная теория сравнивается с результатами компьютерного моделирования, проведенного в университете г. Эдинбург, для определения области применимости теории. Показано, что полученные аналитические выражения могут быть успешно применены в достаточно широкой области концентраций феррочастиц с умеренными межчастичными диполь-дипольными взаимодействиями, сравнимыми с тепловой энергией. Проанализировано типичное поведение парной функции распределения и структурного фактора в зависимости от гранулометрического состава в системе. Структурный фактор, полученный аналитически, сравнивается с результатами эксперимента.

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Neste trabalho, a estrutura local e média de nanopartículas foi estudada utilizando-se métodos de espalhamento e difração de raios X. Os métodos utilizados foram: Análise da Função de Distribuição de Pares Atômicos (Atomic Pair Distribution Function Analysis, em inglês) para o estudo do ordenamento estrutural de curto alcance, Refinamento de Rietveld e Modelamento Total do Perfil de Difração de Pó para o estudo do ordenamento médio. Os materiais estudados foram: nanopartículas de KY3F10 dopadas com Tb, nanocubos núcleo-camada (core-shell, em inglês) de FeO-Fe3O4 e nanopartículas de ferritas de Mn-Zn. O trabalho teve como objetivo demonstrar como os métodos mencionados podem ser utilizados de forma complementar para fornecer informações de curto, médio e longo alcance usando-se dados de espalhamento e difração de raios X. Neste trabalho, ressalta-se a importância de cada método no estudo da estrutura cristalina e demonstra avanço e desenvolvimento de metodologias para a sua aplicação. / In this work, local and average structure of nanoparticles were studied using X-ray scattering and diffraction methods. The methods used were: Atomic Pair Distribution Function Analysis to study the short-range ordering, Rietveld refinement and Whole Powder Pattern Modelling to study the long-range ordering. The studied materials were: Tb-doped KY3F10 nanoparticles, core-shell FeO-Fe3O4 nanocubes and Mn-Zn ferrite nanoparticles. The objective of this work was to demonstrate how the methods mentioned can be used in a complementary way to provide short, average and long range information about the structure using X-ray scattering and diffraction data. The importance of each method to study the crystalline structure is highlighted demonstrating progress and development of methodologies for its application.