Zugl.: Basel, Univ., Diss., 2003

>Magister Scientiae - MSc / Bank asset management mainly involves profit maximization through invest- ment in loans giving high returns on loans, investment in securities for reducing risk and providing liquidity needs. In particular, commercial banks grant loans to creditors who pay high interest rates and are not likely to default on their loans. Furthermore, the banks purchase securities with high returns and low risk. In addition, the banks attempt to lower risk by diversifying their asset portfolio. The main categories of assets held by banks are loans, treasuries (bonds issued by the national treasury), reserves and intangible assets. In this mini-thesis, we solve an optimal asset allocation problem in banking under the mean-variance frame work. The dynamics of the different assets are modelled as geometric Brownian motions, and our optimization problem is of the mean- variance type. We assume the Basel II regulations on banking supervision. In this contribution, the bank funds are invested into loans and treasuries with the main objective being to obtain an optimal return on the bank asset port- folio given a certain risk level. There are two main approaches to portfolio optimization, which are the so called martingale method and Hamilton Jacobi Bellman method. We shall follow the latter. As is common in portfolio op- timization problems, we obtain an explicit solution for the value function in the Hamilton Jacobi Bellman equation. Our approach to the portfolio prob- lem is similar to the presentation in the paper [Hojgaard, B., Vigna, E., 2007. Mean-variance portfolio selection and efficient frontier for defined contribution pension schemes. ISSN 1399-2503. On-line version ISSN 1601-7811]. We pro- vide much more detail and we make the application to banking. We illustrate our findings by way of numerical simulations.

Esta tese apresenta, o projeto de uma perfuratriz que permite a execução de cinco tipos de fundação profunda, e o desenvolvimento de um ensaio de campo que possibilita avaliar as resistências por atrito lateral desenvolvidas entre o instrumento envolvido pelo solo escavado e o terreno natural. A perfuratriz foi projetada para executar estacas dos tipos hélice contínua monitorada, escavadas com trado mecânico, hélice segmentada monitorada, raiz e hollow-auger. As estacas dos tipos hélice contínua monitorada e as escavadas com trado mecânico são muito utilizadas no Brasil; as estacas raiz e hollow-auger são utilizadas em situações especiais e a estaca hélice segmentada monitorada é mais recente, mas sua aplicação tem tido um crescimento importante nos últimos dez anos. Para a perfuratriz multifuncional são apresentados cálculos e desenhos básicos dos principais conjuntos. Para a nova investigação de campo, denominada FDT - Full Displacement Test, é apresentado um desenvolvimento teórico com base no princípio universal da conservação de energia que, em termos práticos, resulta na obtenção da parcela de atrito lateral, denominado atrito lateral unitário equivalente (fse). Os resultados obtidos a partir dos dados aquisitados pelo sistema de monitoramento eletrônico da perfuratriz apresentaram-se concordantes entre si, indicando a possibilidade de praticamente se conseguir a repetibilidade do ensaio. Entre os diversos ensaios realizados, foi dada ênfase aos ensaios realizados no campo experimental de Fundações e Geotecnia da Faculdade de Engenharia Agrícola FEAGRI, da Universidade de Campinas - UNICAMP e foram feitas correlações com as resistências obtidas nas provas de carga estáticas realizadas no local por Albuquerque (2001), a partir dos ajustes feitos para o nível instrumentado na profundidade de 11,70 m para o qual foi determinado um fator (G2), para cada tipo de estaca ensaiada (escavada, hélice contínua e ômega). A partir dos ajustes feitos para o nível 11,70 m foram feitas previsões de capacidade de carga por atrito lateral para os outros níveis instrumentados (5,00 m; 11,10 m e 12,00 m), sendo que os resultados apresentaram-se concordantes. / This thesis presents the design of a drilling rig that allows the execution of five types of deep foundation, and the development of a field test that allows measuring the skin friction resistance developed between the instrument involved by the excavated ground and the natural soil. The drilling rig was designed to make continuous flight auger, bored pile, continuous flight auger with segmented auger, root pile and hollow-auger pile. The continuous flight auger and bored piles are widely used in Brazil; the root pile and hollow-auger pile are used for in special conditions, and the continuous flight auger with segmented auger, is although more recent, but its application has had increased application grown in over the last ten years. For the multifunctional drilling rig, calculations and basic designs of the main sets are presented. For the new field test denominated FDT - Full Displacement Test, a theoretical development based on the universal principle of energy conservation was made carried out resulting and the result, in practical terms, was to obtain in the attainment of the skin friction defined in this thesis as equivalent unit skin friction (fse). The results obtained from the data acquired by the electronic monitoring system of drilling rigs were consistent among themselves, indicating the possibility of practically achieve the repeatability of the test. Among the various tests performed, emphasis was given to tests in the experimental field of foundations and geotechnics, of the College of Agricultural Engineering FEAGRI, Campinas University UNICAMP, and were correlated to the skin friction resistance obtained from the static load tests performed on site by Albuquerque (2001), based on the adjustments done to the instrumented level depth of 11.70 m, for which a factor (G2) was given in each type tested (bored, C.F.A and omega). From the adjustments made to the 11,70 m level, load-bearing capacity of skin friction predictions were made for other instrumented levels (5.00 m; 11.10 m and 12.00 m) presenting consistent results.

O ensaio de simples reconhecimento de solos (SPT) é a ferramenta de investigação de solos mais utilizada no mundo. Devido ao grande número de parâmetros que influenciam os seus resultados, a medida de sua eficiência passa a ser indispensável à transposição de experiências entre as práticas desenvolvidas em diferentes locais. Infelizmente, a medida da eficiência através da instrumentação do impacto do martelo é economicamente inviável para a maioria das empresas de sondagem no Brasil. Este trabalho apresenta uma metodologia para a determinação da eficiência do SPT baseada no princípio de Hamilton e na realização de prova de carga estática sobre o amostrador, que pode ser uma alternativa para sanar esta situação. / The standard penetration test (SPT) is the most used soil investigation tool in the world. Due to the great number of variables that influences its results, the measurement of the efficiency becomes imperative to the transposition of experiences between developed practices in different places. Unfortunately, the measurement of the efficiency through the instrumentation of the hammer impact is economically inpracticable to most of the soil investigation firms in Brazil. This work presents a methodology to determinate the SPT efficiency based on the Hamilton\'s principle and on the execution of static load test over the sampler, what seems to be a good alternative to end this situation.

Cette thèse se compose de deux parties principales. Dans la première partie, le Chapitre 3 est consacré à l'étude du comportement limite d'un système contrôlé singulièrement perturbé avec deux variables d'état qui sont faiblement couplées. Afin de prouver notre résultat d'approximation, nous utilisons la méthode de moyennisation et un résultat récent sur le contrôle nonexpansif. La principale nouveauté de notre approche est de permettre la dynamique limite de dépendre de l'état initial du système rapide. Notons que dans la littérature, le comportement limite d'un tel système a été généralement traité dans des conditions qui garantissent que la limite est indépendante de l'état initial du système rapide. Dans le Chapitre 4, nous généralisons les résultats du Chapitre 3 supposant une condition de nonexpansivité plus générale. De plus, nous considérons un exemple ou la nouvelle condition de nonexpansivité est satisfaite, mais pas la condition de nonexpansivité du Chapitre 3. Dans la deuxième partie de la thèse, le Chapitre 5 porte sur les représentations stables des Hamiltoniens convexes associant à un Hamiltonien donné des fonctions correspondant au problème de Bolza en controle optimal. Dans le Chapitre 6 nous étudions également la stabilité des solutions des équations d'Hamilton-Jacobi-Bellman sous contraintes d'état en exploitant la stabilité des fonctions valeur d'une famille de problèmes de contrôle optimal de Bolza sous contraintes d'état. Nous montrons que sous des hypothèses appropriées, la fonction valeur est la solution unique d'équation d'Hamilton-Jacobi-Bellman et que les solutions sont stables par rapport à l'Hamiltonien et les contraintes d'état. / This thesis consists of two main parts. In the first part, Chapter 3 is devoted to the investigation of the limit behavior of a singularly perturbed control system with two state variables which are weakly coupled. In order to prove our approximation result we use the so called averaging method and a recent result on nonexpansive control. The main novelty of our averaging approach lies in the fact that the limit dynamic may depend on the initial condition of the fast system. In the literature, the investigation of the limit behavior of such systems has been usually addressed under conditions that ensure that the limit dynamic is independent from the initial condition of the fast system. In Chapter 4, we generalise the results of Chapter 3 by considering a more general nonexpansivity condition. Moreover, we consider an example where the new nonexpansity condition is satisfied but the nonexpansivity condition of Chapter 3 does not hold true. The second part deals with Hamilton-Jacobi equations under state constraints. Chapter 5 focuses on the stable representation of convex Hamiltonians by functions describing a Bolza optimal control problem. In Chapter 6 we investigate stability of solutions of Hamilton-Jacobi-Bellman equations under state constraints by studying stability of value functions of a suitable family of Bolza optimal control problems under state constraints. We show that under suitable assumptions, the value function is a unique viscosity solution to Hamilton-Jacobi-Bellman equation and that solutions are stable with respect to Hamiltonians and state constraints.

Das Thema dieser Arbeit ist die spektraltheoretische Untersuchung von zufälligen Operatoren, die zu einem minimal ergodischen bzw. strikt ergodischen Delone dynamischen System assoziiert sind. Es werden kontinuierliche sowie diskrete Modelle untersucht. Diese Modelle sind mathematische Modelle zur Beschreibung von Festkörpern, bei denen die Punkte der einzelnen, in einem Delone dynamischen System enthaltenen, Delone-Mengen die Atompositionen eines Festkörpers beschreiben. Delone-Mengen, die in einem minimal ergodischen Delone dynamischen System enthalten sind weisen eine sehr hohe Ordnungsstruktur auf, sind aber nicht notwendigerweise periodisch. Sie können daher zur Modellierung von Quasikristallen verwendet werden. In dieser Arbeit wird das Spektrum der assoziierten Operatoren im kontinuierlichen sowie im diskreten Fall untersucht.

Es wird Anderson-Lokalisierung und starke dynamische Lokalisierung für Quantengraphen mit Gitterstruktur mit Multiskalenanalyse bewiesen. Für eine weitere Klasse von Quantengraphen wird eine lineare Wegner-Abschätzung gezeigt, woraus die Lipschitz-Stetigkeit der integrierten Zustandsdichte folgt.

The first part of this work gives an introduction into aperiodic order in general and the lines of research pursued. The second part consists of eight manuscripts.

Es wird Anderson-Lokalisierung und starke dynamische Lokalisierung für Quantengraphen mit Gitterstruktur mit Multiskalenanalyse bewiesen. Für eine weitere Klasse von Quantengraphen wird eine lineare Wegner-Abschätzung gezeigt, woraus die Lipschitz-Stetigkeit der integrierten Zustandsdichte folgt.

We consider large and sparse eigenproblems where the spectrum exhibits special symmetries. Here we focus on Hamiltonian symmetry, that is, the spectrum is symmetric with respect to the real and imaginary axes. After briefly discussing quadratic eigenproblems with Hamiltonian spectra we review structured Krylov subspace methods to aprroximate parts of the spectrum of Hamiltonian operators. We will discuss the optimization of the free parameters in the resulting symplectic Lanczos process in order to minimize the conditioning of the (non-orthonormal) Lanczos basis. The effects of our findings are demonstrated for several numerical examples.