Notre thèse propose d'étudier la précision des calculs par la méthode des éléments finis (MEF) au moyen "d'indicateurs de qualité". Les indicateurs de qualité représentent des formules simples qui permettent d'évaluer la qualité des calculs par éléments finis. La qualité de l'analyse numérique est évaluée par rapport à la discrétisation. Le modèle mathématique est considéré correct et les erreurs résultant du choix des propriétés des matériaux ne sont pas pris en compte. Nous avons défini les formulations mathématiques de ces indicateurs de qualité, ainsi que leurs limites inférieures et supérieures. Grâce au choix de formulations simples, il est facile de les introduire dans un logiciel de calcul par éléments finis. Ils ont été implémentés dans le code de calcul CESAR-LCPC, module Mécanique en Comportement Non Linéaire. Afin de démontrer qu'ils ont été correctement définis et de tester leur fiabilité, ces indicateurs de qualité sont testés sur un certain nombre de problèmes simples en 2D et en 3D. Après avoir prouvé leur capacité à caractériser la qualité de la discrétisation des modèles d'éléments finis, nous les avons testés sur le cas d'une excavation de palplanches butonnées (site expérimental de Hochstetten, près de Karlsruhe). La précision des résultats en termes de propriétés mécaniques choisies pour le sol et les structures n'a pas été étudiée. Nous avons également démontré que les résultats sont indépendants des propriétés mécaniques choisies pour le sol ou la structure / The thesis proposes to study the accuracy of the finite element method (FEM) analyses by means of « quality indicators ». The quality indicators represent simple mathematical formulas that are designed to evaluate the reliability of the numerical analyses. The accuracy of the discretization modeling of these analyses is determined ; the mathematical model is considered correct and the errors resulting from the choice of the mechanical properties of the soil are not taken into account. We proposed the mathematical formulations of the quality indicators and also established their lower and upper bounds. Due to their simple mathematical formulation, the quality indicators are easily implemented in any finite element computer code. We have introduced them in the CESAR-LCPC finite element computer code, namely in the nonlinear mechanical execution module. The proposed quality indicators are used on a number of simple 2D and 3D problems elastic and elastoplastic problems in order to assess the jump in stress values in the nodes of the generated mesh. After testing the accuracy of the discretization modeling of these numerical analyses, we evaluated the discretization modeling quality of a braced sheetpile excavation (Hochstetten experimental site, near Karlsruhe). The accuracy of the results based on the mechanical properties of the soil and the structure has not been studied. Also, we proved that the quality indicator results are independent of the chosen mechanical properties for the soil or structure

>Magister Scientiae - MSc / This dissertation studies the computation methods of pricing of Asian options. Asian options are options in which the underlying variable is the average price over a period of time. Because of this, Asian options have a lower volatility and this render them cheaper relative to their European counterparts. Asian options belong to the so-called path-dependent derivatives; they are among the most difficult to price and hedge both analytically and numerically. In practice, it is only discrete Asian options that are traded, however continuous Asian options are used for studying purposes. Several approaches have been proposed in the literature, including Monte Carlo simulations, tree-based methods, Taylor’s expansion, partial differential equations, and analytical ap- proximations among others. When using partial differential equations for pricing of continuous time Asian options, the high dimensionality is problematic. In this dissertation we focus on the discrete time methods. We start off by explaining the binomial tree method, and our last chapter presents the very exciting and relatively simple method of Tsao and Huang, using Taylor approximations. The main papers that are used in this dissertation are articles by Jan Vecer (2001); LCG Rogers (1995); Eric Benhamou (2001); Gianluca Fusai (2007); Kamizono, Kariya and Nakatsuma (2006) and Tsao and Huang (2007). The author has provided computations, including graphs and tables dispersed over the different chapters, to demonstrate the utility of the methods. We observe various parameters of influence such as correlation, volatility, strike, etc. A further contribution by the author of this dissertation is, in particular, in Chapter 5, in the presentation of the work of Tsao et al. Here we have provided slightly more detailed explanations and again some further computational tables.

Synchronizace inflačních cyklů je jednou z podmínek teorie optimální měnové unie, a jelikož bude jednoho dne valná většina členských států EU používat euro, zdá se analýza konvergence jejich inflačních měr jako rozumná i z dnešního pohledu. Používáme data měřítka harmonizovaného indexu spotřebitelských cen, jakož i velmi flexibilní model zdánlivě nesouvisejících regresních modelů a podáváme důkaz o všeobecně rozšířeném, setrvalém a robustním výskytu konvergence inflace v celé EU mezi lety 1999 a 2016. Navíc nám naše metodologie umožňuje zahrnout do modelu řadu dummy proměnných indikujících konkrétní období s možným dopadem na konvergenci inflace. V tomto smyslu ukazujeme, že měnové režimy zaměřené na cenovou stabilitu (inflační cílování, opatření omezující pohyb měnového kurzu) mají příznivý dopad, období globální finanční krize a nulové dolní meze se obecně nejeví jako rušivé, zatímco efekt zavádění společného evropského práva zůstává nejistý. Naše hlavní závěry implikují, že synchronizace inflace zřejmě nepředstavuje problém pro další rozšíření Eurozóny.

The paper examines the hypothesis that the devaluation of the domestic currency leads to the higher exchange rate pass-through at the zero lower bound since the interest rate channel cannot offset effects of the depreciation in that situation. Time-varying vector autoregression with stochastic volatility is used to identify the development of the pass-through. The hypothesis is tested on the Czech dataset because the Czech Republic is considered as the prototypical small open economy with inflation targeting. The assumption of higher pass-through to consumer prices at the zero lower bound is rejected. Obtained results confirm that the deprecation stimulates output growth slightly more when the interest rate is close to zero. Our estimations imply that the exchange rate commitment of the Czech National Bank increased the price level by 0.116 % and contributed to the output growth by 0.781 %.

Cette thèse présente plusieurs extensions relatives aux modèles affines positifs de taux d'intérêt. Un premier chapitre introduit les concepts reliés aux modélisations employées dans les chapitres suivants. Il détaille la définition de processus dits affines, et la construction de modèles de prix d'actifs obtenus par non-arbitrage. Le chapitre 2 propose une nouvelle méthode d’estimation et de filtrage pour les modèles espace-état linéaire-quadratiques. Le chapitre suivant applique cette méthode d’estimation à la modélisation d’écarts de taux interbancaires de la zone Euro, afin d’en décomposer les fluctuations liées au risque de défaut et de liquidité. Le chapitre 4 développe une nouvelle technique de création de processus affines multivariés à partir leurs contreparties univariées, sans imposer l’indépendance conditionnelle entre leurs composantes. Le dernier chapitre applique cette méthode et dérive un processus affine multivarié dont certaines composantes peuvent rester à zéro pendant des périodes prolongées. Incorporé dans un modèle de taux d’intérêt, ce processus permet de rendre compte efficacement des taux plancher à zéro. / This thesis presents new developments in the literature of non-negative affine interest rate models. The first chapter is devoted to the introduction of the main mathematical tools used in the following chapters. In particular, it presents the so-called affine processes which are extensively employed in no-arbitrage interest rate models. Chapter 2 provides a new filtering and estimation method for linear-quadratic state-space models. This technique is exploited in the 3rd chapter to estimate a positive asset pricing model on the term structure of Euro area interbank spreads. This allows us to decompose the interbank risk into a default risk and a liquidity risk components. Chapter 4 proposes a new recursive method for building general multivariate affine processes from their univariate counterparts. In particular, our method does not impose the conditional independence between the different vector elements. We apply this technique in Chapter 5 to produce multivariate non-negative affine processes where some components can stay at zero for several periods. This process is exploited to build a term structure model consistent with the zero lower bound features.

This diploma thesis describes the Quantitative easing as an unconvetional tool of the monetary policy. In the first chapter of this thesis there is theoretical analysis of the zero lower bound and also of specific phenomenon that might occur in this situation (the liquidity trap). The second chapter deals with the quantitative easing as a monetary policy with focus on the United States. It summarizes its development during three so called rounds, during which the quantitative easing has been used. This chapter also contains analysis of the entrance and exit strategy of the quantitative easing. In the third chapter, there is an econometric model estimated by ordinary least squares method with robust errors. This model is being used to verify the hypothesis whether the quantitative easing lowered long-term interest rates. The hypothesis has been rejected as the quantitative easing does not have statistically significant effect on any selected long-term bonds.

The main purpose of this thesis is to analyse the impacts of unconventional monetary policy instruments on small open economies in zero lower-bound situations. Although all unconventional instruments are discussed, an emphasis is placed on currency intervention. Impacts of the various instruments are demonstrated using the economies of Czech Republic and Switzerland as case studies. The thesis will conclude with a comparison of the case studies.

The amount of carbon dioxide in the Earth’s atmosphere has significantly increased in the last few decades as compared to the last 80,000 years approximately. The increase in carbon dioxide levels are affecting the temperature and therefore need to be understood better. In order to study the effects of global events on the carbon dioxide levels, one need to properly estimate the trends in carbon dioxide in the previous years. In this project, we will perform the task of estimating the trend in carbon dioxide measurements taken in Mauna Loa for the last 46 years, also known as the Keeling Curve, using estimation techniques based on a Taylor and Fourier series model equation. To perform the estimation, we will employ Maximum Likelihood Estimation (MLE) and the Cramér-Rao Lower Bound (CRLB) and review our results by comparing it to other estimation techniques. The estimation of the trend in Keeling Curve is well-posed however, the estimation for the first derivative of the trend is an ill-posed problem. We will further calculate if the estimation error is under a suitable limit and conduct statistical analyses for our estimated results.

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Indoor positioning is desired in many areas for various reasons, such as positioning products in industrial environments, hospital equipment or firefighters inside a building on fire. One even tougher situation where indoor positioning can be useful is locating a specific object on a shelf in a commercial setting. This thesis aims to investigate and design different network deployment strategies in an indoor environment in order to achieve both high position estimation accuracy and availability. The investigation considers the two positioning techniques downlink time difference of arrival, DL-TDOA, and round trip time, RTT. Simulations of several deployments are performed in two standard scenarios which mimic an indoor open office and an indoor factory, respectively. Factors having an impact on the positioning accuracy and availability are found to be deployment geometry, number of base stations, line-of-sight conditions and interference, with the most important being deployment geometry. Two deployment strategies are designed with the goal of optimising the deployment geometry. In order to achieve both high positioning accuracy and availability in a simple, sparsely cluttered environment, the strategy is to deploy the base stations evenly around the edges of the deployment area. In a more problematic, densely cluttered environment the approach somewhat differs. The proposed strategy is now to identify and strategically place some base stations in the most cluttered areas but still place a majority of the base stations around the edges of the deployment area. A robust positioning algorithm is able to handle interference well and to decrease its impact on the positioning accuracy. The cost, in terms of frequency resources, of using more orthogonal signals may not be worth the small improvement in accuracy and availability.