Conic finance is a brand new quantitative finance theory. The thesis is on the applications of conic finance on South African Financial Markets. Conic finance gives a new perspective on the way people should perceive financial markets. Particularly in incomplete markets, where there are non-unique prices and the residual risk is rampant, conic finance plays a crucial role in providing prices that are acceptable at a stress level. The theory assumes that price depends on the direction of trade and there are two prices, one for buying from the market called the ask price and one for selling to the market called the bid price. The bid-ask spread reects the substantial cost of the unhedgeable risk that is present in the market. The hypothesis being considered in this thesis is whether conic finance can reduce the residual risk? Conic finance models bid-ask prices of cashows by applying the theory of acceptability indices to cashows. The theory of acceptability combines elements of arbitrage pricing theory and expected utility theory. Combining the two theories, set of arbitrage opportunities are extended to the set of all opportunities that a wide range of market participants are prepared to accept. The preferences of the market participants are captured by utility functions. The utility functions lead to the concepts of acceptance sets and the associated coherent risk measures. The acceptance sets (market preferences) are modeled using sets of probability measures. The set accepted by all market participants is the intersection of all the sets, which is convex. The size of this set is characterized by an index of acceptabilty. This index of acceptability allows one to speak of cashows acceptable at a level, known as the stress level. The relevant set of probability measures that can value the cashows properly is found through the use of distortion functions. In the first chapter, we introduce the theory of conic finance and build a foundation that leads to the problem and objectives of the thesis. In chapter two, we build on the foundation built in the previous chapter, and we explain in depth the theory of acceptability indices and coherent risk measures. A brief discussion on coherent risk measures is done here since the theory of acceptability indices builds on coherent risk measures. It is also in this chapter, that some new acceptability indices are introduced. In chapter three, focus is shifted to mathematical tools for financial applications. The chapter can be seen as a prerequisite as it bridges the gap from mathematical tools in complete markets to incomplete markets, which is the market that conic finance theory is trying to exploit. As the chapter ends, models used for continuous time modeling and simulations of stochastic processes are presented. In chapter four, the attention is focussed on the numerical methods that are relevant to the thesis. Details on obtaining parameters using the maximum likelihood method and calibrating the parameters to market prices are presented. Next, option pricing by Fourier transform methods is detailed. Finally a discussion on the bid-ask formulas relevant to the thesis is done. Most of the numerical implementations were carried out in Matlab. Chapter five gives an introduction to the world of option trading strategies. Some illustrations are used to try and explain the option trading strategies. Explanations of the possible scenarios at the expiration date for the different option strategies are also included. Chapter six is the appex of the thesis, where results from possible real market scenarios are presented and discussed. Only numerical results were reported on in the thesis. Empirical experiments could not be done due to limitations of availabilty of real market data. The findings from the numerical experiments showed that the spreads from conic finance are reduced. This results in reduced residual risk and reduced low cost of entering into the trading strategies. The thesis ends with formal discussions of the findings in the thesis and some possible directions for further research in chapter seven. / Thesis (MSc (Risk Analysis))--North-West University, Potchefstroom Campus, 2013.

Conic finance is a brand new quantitative finance theory. The thesis is on the applications of conic finance on South African Financial Markets. Conic finance gives a new perspective on the way people should perceive financial markets. Particularly in incomplete markets, where there are non-unique prices and the residual risk is rampant, conic finance plays a crucial role in providing prices that are acceptable at a stress level. The theory assumes that price depends on the direction of trade and there are two prices, one for buying from the market called the ask price and one for selling to the market called the bid price. The bid-ask spread reects the substantial cost of the unhedgeable risk that is present in the market. The hypothesis being considered in this thesis is whether conic finance can reduce the residual risk? Conic finance models bid-ask prices of cashows by applying the theory of acceptability indices to cashows. The theory of acceptability combines elements of arbitrage pricing theory and expected utility theory. Combining the two theories, set of arbitrage opportunities are extended to the set of all opportunities that a wide range of market participants are prepared to accept. The preferences of the market participants are captured by utility functions. The utility functions lead to the concepts of acceptance sets and the associated coherent risk measures. The acceptance sets (market preferences) are modeled using sets of probability measures. The set accepted by all market participants is the intersection of all the sets, which is convex. The size of this set is characterized by an index of acceptabilty. This index of acceptability allows one to speak of cashows acceptable at a level, known as the stress level. The relevant set of probability measures that can value the cashows properly is found through the use of distortion functions. In the first chapter, we introduce the theory of conic finance and build a foundation that leads to the problem and objectives of the thesis. In chapter two, we build on the foundation built in the previous chapter, and we explain in depth the theory of acceptability indices and coherent risk measures. A brief discussion on coherent risk measures is done here since the theory of acceptability indices builds on coherent risk measures. It is also in this chapter, that some new acceptability indices are introduced. In chapter three, focus is shifted to mathematical tools for financial applications. The chapter can be seen as a prerequisite as it bridges the gap from mathematical tools in complete markets to incomplete markets, which is the market that conic finance theory is trying to exploit. As the chapter ends, models used for continuous time modeling and simulations of stochastic processes are presented. In chapter four, the attention is focussed on the numerical methods that are relevant to the thesis. Details on obtaining parameters using the maximum likelihood method and calibrating the parameters to market prices are presented. Next, option pricing by Fourier transform methods is detailed. Finally a discussion on the bid-ask formulas relevant to the thesis is done. Most of the numerical implementations were carried out in Matlab. Chapter five gives an introduction to the world of option trading strategies. Some illustrations are used to try and explain the option trading strategies. Explanations of the possible scenarios at the expiration date for the different option strategies are also included. Chapter six is the appex of the thesis, where results from possible real market scenarios are presented and discussed. Only numerical results were reported on in the thesis. Empirical experiments could not be done due to limitations of availabilty of real market data. The findings from the numerical experiments showed that the spreads from conic finance are reduced. This results in reduced residual risk and reduced low cost of entering into the trading strategies. The thesis ends with formal discussions of the findings in the thesis and some possible directions for further research in chapter seven. / Thesis (MSc (Risk Analysis))--North-West University, Potchefstroom Campus, 2013.

Thesis (M.B.A.)--University of Hong Kong, 1992.

Ce travail tente de développer des outils numériques efficaces pour une approche plus rationnelle et moins empirique du dimensionnement à la ruine des ouvrages de génie civil. Contrairement aux approches traditionnelles reposant sur une combinaison de calculs élastiques, l'adoption de coefficients de sécurité et une vérification locale des sections critiques, la théorie du calcul à la rupture nous semble être un outil prometteur pour une évaluation plus rigoureuse de la sécurité des ouvrages. Dans cette thèse, nous proposons de mettre en œuvre numériquement les approches statique par l'intérieur et cinématique par l'extérieur du calcul à la rupture à l'aide d'éléments finis dédiés pour des structures de plaque en flexion et de coque en interaction membrane-flexion. Le problème d'optimisation correspondant est ensuite résolu à l'aide du développement, relativement récents, de solveurs de programmation conique particulièrement efficaces. Les outils développés sont également étendus au contexte de l'homogénéisation périodique en calcul à la rupture, qui constitue un moyen performant de traiter le cas des structures présentant une forte hétérogénéité de matériaux. Des procédures numériques sont spécifiquement développées afin de déterminer puis d'utiliser dans un calcul de structure des critères de résistance homogènes équivalents. Enfin, les potentialités de l'approche par le calcul à la rupture sont illustrées sur deux exemples complexes d'ingénierie : l'étude de la stabilité au feu de panneaux en béton armé de grande hauteur ainsi que le calcul de la marquise de la gare d'Austerlitz / This work aims at developping efficient numerical tools for a more rational and less empirical assessment of civil engineering structures yield design. As opposed to traditionnal methodologies relying on combinations of elastic computations, safety coefficients and local checking of critical members, the yield design theory seems to be a very promising tool for a more rigourous evaluation of structural safety. Lower bound static and upper bound kinematic approaches of the yield design theory are performed numerically using dedicated finite elements for plates in bending and shells in membrane-bending interaction. Corresponding optimization problems are then solved using very efficient conic programming solvers. The proposed tools are also extended to the framework of periodic homogenization in yield design, which enables to tackle the case of strong material heterogeneities. Numerical procedures are specifically tailored to compute equivalent homogeneous strength criteria and to use them, in a second step, in a computation at the structural level. Finally, the potentialities of the yield design approach are illustrated on two complex engineering problems : the stability assessment of high-rise reinforced concrete panels in fire conditions and the computation of the Paris-Austerlitz railway station canopy

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-17T12:22:57Z No. of bitstreams: 1 arquivototal.pdf: 697305 bytes, checksum: 0b28f8f8c4f8b4509047eb441817be7c (MD5) / Made available in DSpace on 2017-08-17T12:22:57Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 697305 bytes, checksum: 0b28f8f8c4f8b4509047eb441817be7c (MD5) Previous issue date: 2016-03-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we present an explicit geometric characterization for the space of quadratcs form vanishing precisely on a twisted cubic. We show that the set of degenerate quadrics lying on a net of quadrics containing a twisted cubic is described by a curve whose equation is given by the square of an irreducible conic. Conversely, if is a net of quadrics whosw intersection with the set of degenerate quadrics is a curve given by the square of an irreducible conic, we furnish conditions under which the cammon zero locus of turns out to be a twisted cubic. It is enough to require that does not contain a pair of planes. / Neste trabalho, apresentamos uma caracteriza c~ao geom etrica expl cita para o espa co das formas quadr aticas que se anulam precisamente sobre uma c ubica reversa. Mostramos que o conjunto das qu adricas degeneradas pertencentes a uma rede de qu adricas que cont em a c ubica reversa e descrita por uma curva cuja equa c~ao e dada pelo quadrado de uma c^onica irredut vel. Rec procamente, se e uma rede de qu adricas cuja interse c~ao com o conjunto das qu adricas n~ao degeneradas e uma curva dada pelo quadrado de uma c^onica irredut vel, fornecemos condi c~oes sob as quais o lugar dos zeros comuns de seja uma c ubica reversa. E su ciente que n~ao contenha um par de plano.

Made available in DSpace on 2014-12-17T15:04:48Z (GMT). No. of bitstreams: 1 MartaMMM.pdf: 1215431 bytes, checksum: a4bc80e0c6dcb3570e856b3f35916003 (MD5) Previous issue date: 2007-04-24 / In this work, the didactical possibilities of investigation use in classroom, through an experience with high school students from Federal Center of Technological Education of Para?ba, as well as the study of conic sections were analysed. In order to fulfill our goals the theoretical conceptions concerning the meaninful learning in conection with the investigation of mathematics history were taken into account. The classroom research occurred by means of activities which encouraged the learner to investigate his own concepts on the conic sections. The results of the proposed activities showed the effectiveness and the efficiency of such a methodology as regards the making up of the required knowledge. They also reveal that the investigation in the classroom guides the ones involved, in this process, to have a wider look at the origins, the methods used and the several representations presented by mathematics that certainly lead, specially the students, to a meaninful learning / Neste trabalho, analisamos as possibilidades did?ticas de uso da investiga??o em sala de aula, a partir de uma experi?ncia com estudantes do ensino m?dio no Centro Federal de Educa??o Tecnol?gica da Para?ba CEFET PB, na qual abordamos o estudo das sec??es c?nicas. Para o alcance dos nossos objetivos tomamos como aporte te?rico as concep??es referentes ? aprendizagem significativa em conex?o com a investiga??o em hist?ria da matem?tica. A pesquisa em sala de aula efetivou-se atrav?s de atividades que instigaram, no aprendiz, o desejo de investigar os conceitos pr?prios das sec??es c?nicas. Os resultados das atividades propostas e postas em pr?tica mostraram a efic?cia e a efici?ncia de tal metodologia na constru??o do conhecimento requerido, nos mostrando que a investiga??o em sala de aula conduz os envolvidos, nesse processo, a olhar de forma mais globalizante para as origens e os m?todos utilizados para desenvolver, al?m das v?rias representa??es apresentadas pela matem?tica, o que, certamente conduz, principalmente os alunos, a uma aprendizagem significativa

[pt] Esse trabalho propõe uma implementação numérica para otimização de forma em problemas bi-dimensionais de elasticidade. O objetivo principal é propor uma metodologia eficiente e robusta para solução de problemas de otimização de forma considerando a minimização de concentração de tensões. Na implementação proposta, a análise estrutural é realizada pelo Método dos Elementos de Contorno Simétrico de Galerkin (MECSG), evitando-se assim a dispendiosa etapa de geração da malha. A avaliação das tensões no contorno é obtida por meio de um método preciso, ideal para problemas com concentrações de tensões. Outro aspecto relevante na implementação é a adequada partição das equações do MECSG de forma a reduzir, consideravelmente, o esforço computacional associado à etapa da análise estrutural. O problema de otimização é resolvido utilizando-se um método de otimização moderno, conhecido como Programação Cônica de Segunda Orderm (PCSO). Especificamente, busca-se a reposta do problema de otimização não linear por meio da solução de uma sequência de subproblemas de PCSO. / [en] In this work a numerical implementation of shape optimization in two-dimensional linear elasticity problems is proposed. The main goal is to propose a robust and efficient methodology for the solution of shape optimization problems regarding the minimization of stress concentration effects. In the proposed implementation, the structural analysis is performed by the Symmetric Galerkin Boundary Element Method (SGBEM), thus disposing of the mesh generation burden. The boundary stress evaluation is carried out by an accurate approach which is ideally suited for problems with stress concentrations. Another relevant feature of the proposed implementation is a suitable partition of the SGBEM equations which aims at reducing the computational effort associated with the structural analysis stage. The solution for the optimization problem is obtained by means of a modern numerical optimization method, the so-called Second Order Conic Programming (SOCP). Specifically, the solution for the non-linear optimization is sought by solving a sequence of SOCP subproblems.

Konformen har tidigare under arkitekturhistorien ofta använts för att skapa rum enligt en cellulär logik. Projektet ämnar ompröva användandet av konformen för att organisera rum, i det här fallet applicerat på en konsthall i Solna, genom att gå utanför enbart ett repetitivt arrangemang av vertikala koniska moduler för att uppnå en variation av skalor och riktningar som spänner från stora horisontella koniska rum till mer intima småskaliga vertikala rumsbildningar. Rummen skapas genom en adderande process där koner genomskärs med varandra och med plana element som adderas i operationen. Detta tillåter på så sätt en samexistens av två olika rumsliga logiker vilket leder till en komplex och tillåtande arkitektur som kan svara mot behoven i programmet och som även lyfter fram och förstärker formen hos byggnaden. Projektet utforskar även möjligheterna med att använda konen i egenskap av att vara en enkelkrökt yta och dess betydelse för digital modellering, ritningar och konstruktion. / The cone in architecture has often been used to shape and generate space with a cellular structural logic. This project reconsiders the use of the cone for organizing space, in this case applied on an Art Centre in Solna, going beyond the mere repetitive logic of conic modules, to allow for a variety of scales and directions, ranging from large span horizontal conic spaces to more intimate smaller scaled vertical conic rooms. The spaces are created through an additive process of intersecting cones with planar elements added into the operation, thus allowing the coexistence of two spatial logics, leading towards a manifold and allowing architecture that can handle the requirements of the program and that reinforces the perception of the shape. The project also explores the possibilities of the cone as a single curved unfoldable surface and it’s implications on digital model making, drawing and physical construction.

No description available.

TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra