Submitted by Miriam Lucas (miriam.lucas@unioeste.br) on 2017-08-25T14:09:02Z No. of bitstreams: 2 Adriana Somavilla 2017.pdf: 3635522 bytes, checksum: f64698dbd2b447ae4e2eb4ee3d9df9c6 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-08-25T14:09:02Z (GMT). No. of bitstreams: 2 Adriana Somavilla 2017.pdf: 3635522 bytes, checksum: f64698dbd2b447ae4e2eb4ee3d9df9c6 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-03-13 / Creating an initial teacher training course involves many aspects, among them, the identity of the Teaching Institution and the constitution of the group of teachers involved in this process. In this scenario, some of the issues faced in the initial training courses of a mathematics teacher are related to pedagogical training, to the institutional field and to the curricular field of these courses. One of these impasses is the relation between Mathematics teaching and the development of competences for the exercise of citizenship. In this sense, debates and discussions on the financial literacy of citizens highlight the role of the contemporary school in the dissemination of financial knowledge. In Brazil there is a movement to insert the theme of financial education in Basic Education and although it is a subject of socioeconomic relevance, financial education is not yet contemplated in the political-pedagogical project of most public schools. Even with some initiatives in this direction, what draws attention to the initial training of mathematics teachers is the absence of discussions as to the insertion of the discipline of Financial Mathematics in the Mathematics Degree courses in Brazil. In this context, a relevant research question emerges: What is revealed about the insertion of the discipline of Financial Mathematics in the Mathematics Degree courses of the Federal Institutes of Education, Science and Technology of the South Region of Brazil? Thus, by adopting an analytical phenomenological research posture, it was sought the teachers with initial training in Mathematics, members of the Structuring Teaching Core of these Institutes who participated in the elaboration and modifications of the Political Pedagogical Project of the Mathematics Courses, offered as a classroom course, in 2016. In this search process, through the coordination of the Mathematics Degree courses, fourteen teachers were pointed out as possible research subjects. After being invited to participate in the research, the invitation was accepted by six teachers and the interview occurred with five of them. The interview prioritized the statements and spontaneous manifestations of the participants and the recording regarding the speech of these teachers was taken in video and audio, which were transcribed and analyzed later, following the three reflexive steps with a phenomenological tendency: description, reduction and interpretation. With the help of the Atlas t.i. software, the analysis process was guided by the research question, looking at the units of meaning that emerged from the Teaching Projects of the Courses and from the teachers' testimonials. Following, by the convergences of the units of meaning, two broad categories were perceived, which were described and interpreted separately. In this sense, in a diverse scenario, some aspects emerged in the investigation, such as: the intra-institutionality and its relation to the insertion of the discipline of Financial Mathematics; the standardization of the curriculum; the turnover of teachers in the NDE and the implications on the decisions of the curricular matrix of these courses in this condition; the delineation of the courses curricular matrix dependent on public policies; the non-establishment of the relationship between Financial Mathematics and Financial Education, signaling to the financial literacy of teachers; the estrangement of the courses before the financial context that is presented; among others. In this direction, the investigative look points to a study of proposals that can contribute to improving the level of the citizens' financial literacy. / Na criação de um curso de formação inicial de professores estão envolvidos muitos aspectos, dentre eles, a identidade da Instituição de Ensino e a constituição do grupo de docentes envolvidos nesse processo. Nesse cenário, algumas das questões enfrentadas nos cursos de formação inicial de um professor de matemática estão relacionadas à formação pedagógica, ao campo institucional e ao campo curricular desses cursos. Um desses impasses é a relação entre o ensino de Matemática e o desenvolvimento de competências para o exercício da cidadania. Nesse sentido, debates e discussões sobre a literacia financeira dos cidadãos destacam o papel da escola contemporânea na disseminação do conhecimento financeiro. No Brasil há um movimento de inserção da temática educação financeira na Educação Básica e apesar de ser um tema de relevância socioeconômica, a educação financeira ainda não é contemplada no projeto político-pedagógico da maioria das escolas públicas. Mesmo com algumas iniciativas nessa direção, o que chama a atenção na formação inicial de professores de matemática, é a ausência de discussões quanto à inserção da disciplina de Matemática Financeira nos cursos de Licenciatura em Matemática no Brasil. Nesse contexto, emerge uma interrogação de pesquisa relevante: O que se revela sobre a inserção da disciplina de Matemática Financeira nos cursos de Licenciatura em Matemática dos Institutos Federais de Educação, Ciência e Tecnologia da Região Sul do Brasil? Assim, ao adotar uma postura de investigação de pesquisa analítica de cunho fenomenológico, buscou-se pelos docentes com formação inicial em Matemática integrantes do Núcleo Docente Estruturante desses Institutos que participaram da elaboração e das modificações do Projeto Político Pedagógico dos Cursos (PPC) de Licenciatura em Matemática, ofertados na forma presencial, em 2016. Nesse processo de busca, por meio das coordenações dos cursos de Licenciatura em Matemática, catorze docentes foram apontados como sujeitos passíveis de investigação. Após serem convidados a participar da pesquisa, o convite foi aceito por seis professores e a entrevista ocorreu com cinco deles. A entrevista priorizou os depoimentos e manifestações espontâneas dos participantes e o registro referente ao discurso desses professores se deu por meio de gravação de vídeo e áudio, que foram transcritos e analisados posteriormente, seguindo os três passos reflexivos com tendência fenomenológica: descrição, redução e interpretação. Com o auxílio do software Atlas t.i., o processo de análise foi conduzido pela interrogação de pesquisa, com o olhar para as unidades de significado que emergiram dos Projetos Pedagógicos dos Cursos e dos depoimentos dos docentes. Na sequência, pelas convergências das unidades de significado, foram percebidas duas categorias amplas, que foram descritas e interpretadas separadamente. Nesse sentido, num cenário diverso, despontaram alguns aspectos na investigação, tais como: a intra-institucionalidade e sua relação na inserção da disciplina de Matemática Financeira; a padronização da grade curricular; a rotatividade dos docentes do NDE e as implicações nas decisões da matriz curricular desses cursos nessa condição; o delinear da matriz curricular dos cursos dependente de políticas públicas; o não estabelecimento da relação entre a Matemática Financeira e a Educação Financeira, sinalizando para a literacia financeira dos professores; o distanciamento dos cursos frente ao contexto financeiro que está posto; entre outros. Nessa direção, o olhar investigativo aponta para um estudo de propostas que contribuam para melhorar o nível de literacia financeira dos cidadãos.

Made available in DSpace on 2016-04-27T16:58:29Z (GMT). No. of bitstreams: 1 Nelson Dias Leme.pdf: 5327513 bytes, checksum: 4de15af5883da758e73a3351fa8b55d1 (MD5) Previous issue date: 2007-10-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims to contribute to the investigation of the impact of a constructionist approach to the use of electronic spreadsheets on the teaching and learning of topics related to Financial Mathematics. To this end, a teaching experiment was designed which involved students in the construction of their own formulas, using spreadsheets, for calculating interests and future values of investments, under regimes of both simple and compound rates. The constructionist conceptions of Papert provided a theoretical base for the development of the activities. The methodology adopted for the study was modelled according to the design-based research methodologies. Two phases of experimentation were elaborated. The first phase involves students initiating their studies in Financial Mathematics in working on a set of activities with spreadsheets, and then completing a series of paper and pencil tasks. In the second phase, to provide a basis for comparing the approach adopted with the more usual practice of giving students previously defined formulae for calculating interest, the paper and pencil task were also administered to a group of students who has previously studied Financial Mathematics. The analysis of data followed the cycle of description-execution-reflectiondebugging- description described by Valente. According to these analyses, the formulae constructed by the students and implemented on the computer served as computational models providing feedback and enabling simulations of various possible situations. This in turn allowed students to engage in a cycle of expression, evaluation and reflection of the mathematical domain in question / O objetivo deste trabalho é colaborar na investigação do impacto da abordagem construcionista e das potencialidades das planilhas eletrônicas no ensino-aprendizagem de conteúdos da Matemática Financeira. Para alcançar o objetivo proposto, foi elaborado um experimento de ensino envolvendo alunos na construção de suas próprias fórmulas, usando planilhas eletrônicas, para o cálculo dos juros e do montante, nos regimes dos juros simples e compostos. Para o desenvolvimento das atividades buscamos referência na concepção construcionista de Seymour Papert (1994). A metodologia empregada neste trabalho está baseada no design-based research methodologies . Metodologia de Pesquisa Baseada em Design. Foram desenvolvidas duas fases de experimentação. A primeira fase envolveu um grupo de alunos iniciantes seus em estudos de Matemática Financeira, em um conjunto de atividades com planilhas eletrônicas e, em uma série de tarefas em papel e lápis. Na segunda fase para comparar com o desempenho do primeiro grupo, foram aplicadas as atividades com papel e lápis a um grupo de alunos que já concluiu seus estudos de Matemática Financeira e que vivenciou uma abordagem de ensino onde as fórmulas não foram construídas. A análise empregou o ciclo descrição-execução-reflexão-depuraçãodescrição de Valente (2002). Segundo nossas análises, as fórmulas deduzidas e implementadas no computador são modelos computacionais que possibilitam o feedback e a simulação, favorecendo o envolvimento dos aprendizes no ciclo básico de expressão, avaliação e reflexão sobre o domínio considerado

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Humanities, School of Education, 2013 / Mathematics-for-teaching (MfT) is complex, multi-faceted and topic-specific. In this study, a Financial Mathematics course for pre-service secondary mathematics teachers provides a revelatory case for investigating MfT. The course was designed and taught by the author to a class of forty-two students at a university in South Africa. Eight students, forming a purposive sample, participated as members of two focus tutorial groups and took part in individual and group interviews. As an instance of insider research, the study makes use of a qualitative methodology that draws on a variety of data sources including lecture sessions and group tutorials, group and individual interviews, students’ journals, a test and a questionnaire. The thesis is structured in two parts. The first part explores revisiting of school mathematics with particular focus on compound interest and the related aspects of percentage change and exponential growth. Four cases are presented, in the form of analytic narrative vignettes which structure the analysis and provide insight into opportunities for learning MfT of compound interest. The evidence shows that opportunities may be provided to learn a range of aspects of MfT through revisiting school mathematics. The second part focuses on obstacles experienced by students in learning annuities, their time-related talk, as well as their use of mathematical resources such as timelines and spreadsheets. A range of obstacles are identified. Evidence shows that students use timelines in a range of non-standard ways but that this does not necessarily determine or reflect their success in solving annuities problems. Students’ use of spreadsheets reveals that spreadsheets are a powerful tool for working with annuities. A key finding with regard to teachers’ mathematical knowledge, and which cuts across both parts of the thesis, is the importance of being able to move between compressed and decompressed forms of mathematics. The study makes three key contributions. Firstly, a framework for MfT is proposed, building on existing frameworks in the literature. This framework is used as a conceptual tool to frame the study, and as an analytic tool to explore opportunities to learn MfT as well as the obstacles experienced by. A second contribution is the theoretical and empirical elaboration of the notion of revisiting. Thirdly, a range of theoretical constructs related to teaching and learning introductory financial mathematics are introduced. These include separate reference landscapes for the concepts of compound interest and annuities

Derivative pricing, and in particular the pricing of options, is an important area of current research in financial mathematics. Experts debate on the best method of pricing and the most appropriate model of a price process to use. In this thesis, a ``Switching Black-Scholes'' model of a price process is proposed. This model is based on the standard geometric Brownian motion (or Black-Scholes) model of a price process. However, the drift and volatility parameters are permitted to vary between a finite number of possible values at known times, according to the state of a hidden Markov chain. This type of model has been found to replicate the Black-Scholes implied volatility smiles observed in the market, and produce option prices which are closer to market values than those obtained from the traditional Black-Scholes formula. As the Markov chain incorporates a second source of uncertainty into the Black-Scholes model, the Switching Black-Scholes market is incomplete, and no unique option pricing methodology exists. In this thesis, we apply the methods of mean-variance hedging, Esscher transforms and minimum entropy in order to price options on assets which evolve according to the Switching Black-Scholes model. C programs to compute these prices are given, and some particular numerical examples are examined. Finally, filtering techniques and reference probability methods are applied to find estimates of the model parameters and state of the hidden Markov chain. / Thesis (Ph.D.)--Applied Mathematics, 2003.

<p>In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock.</p>

In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock.

In the first part of our work we focus on the model of the optimal consumption with a random income. We provide the three dimensional equation for this model, demonstrate the reduction to the two dimensional case and provide for two different utility functions the full point-symmetries' analysis of the equations. We also demonstrate that for the logarithmic utility there exists a unique and smooth viscosity solution the existence of which as far as we know was never demonstrated before. In the second part of our work we develop the concept of the empirical liquidity measure. We provide the retrospective view of the works on this issue, discuss the proposed definitions and develop our own empirical measure based on the intuitive mathematical model and comprising several features of the definitions that existed before. Then we verify the measure provided on the real data from the market and demonstrate the advantages of the proposed value for measuring the illiquidity.

One of the major problem faced by banks is how to manage the risk exposure in large portfolios. According to Basel II regulation banks has to measure the risk using Value-at-Risk with confidence level 99%. However, this regulation does not specify the way to calculate Valueat- Risk. The easiest way to calculate Value-at-Risk is to assume that portfolio returns are normally distributed. Altough, this is the most common way to calculate Value-at-Risk, there exists also other methods. The previous crisis shows that the regular methods are unfortunately not always enough to prevent bankruptcy. This paper is devoted to compare the classical methods of estimating risk with other methods such as Cornish-Fisher Expansion (CFVaR) and assuming generalized hyperbolic distribution. To be able to do this study, we estimate the risk in a large portfolio consisting of ten stocks. These stocks are chosen from the NASDAQ 100-list in order to have highly liquid stocks (bluechips). The stocks are chosen from different sectors to make the portfolio welldiversified. To investigate the impact of dependence between the stocks in the portfolio we remove the two most correlated stocks and consider the resulting eight stock portfolio as well. In both portfolios we put equal weight to the included stocks. The results show that for a well-diversified large portfolio none of the risk measures are violated. However, for a portfolio consisting of only one highly volatile stock we prove that we have a violation in the classical methods but not when we use the modern methods mentioned above.

The problem of managing the portfolio provisions is of very high importance for any financial institution. In this paper we provide both static and dynamic models of provisions estimation for the case when the decision about provisions is made at the first moment of time subject to the absence of information and for the case of complete and incomplete information. Also the hedging strategy for the case of the defaultable market is presented in this work as another tool of reducing the risk of default. The default time is modelled as a first-passage time of a standard Brownian motion through a deterministic barrier. Some methods of numerical provision estimation are also presented.

Derivative pricing, and in particular the pricing of options, is an important area of current research in financial mathematics. Experts debate on the best method of pricing and the most appropriate model of a price process to use. In this thesis, a ``Switching Black-Scholes'' model of a price process is proposed. This model is based on the standard geometric Brownian motion (or Black-Scholes) model of a price process. However, the drift and volatility parameters are permitted to vary between a finite number of possible values at known times, according to the state of a hidden Markov chain. This type of model has been found to replicate the Black-Scholes implied volatility smiles observed in the market, and produce option prices which are closer to market values than those obtained from the traditional Black-Scholes formula. As the Markov chain incorporates a second source of uncertainty into the Black-Scholes model, the Switching Black-Scholes market is incomplete, and no unique option pricing methodology exists. In this thesis, we apply the methods of mean-variance hedging, Esscher transforms and minimum entropy in order to price options on assets which evolve according to the Switching Black-Scholes model. C programs to compute these prices are given, and some particular numerical examples are examined. Finally, filtering techniques and reference probability methods are applied to find estimates of the model parameters and state of the hidden Markov chain. / Thesis (Ph.D.)--Applied Mathematics, 2003.