Made available in DSpace on 2018-06-27T19:13:37Z (GMT). No. of bitstreams: 3 Marielen Fatima Caramori.pdf: 1203046 bytes, checksum: 0928217a3ea20a56ebf8d3e8fe259e57 (MD5) Marielen Fatima Caramori.pdf.txt: 187019 bytes, checksum: b0c34cb9e680e6670d359f12d7bf9e61 (MD5) Marielen Fatima Caramori.pdf.jpg: 3224 bytes, checksum: 6bf932517585a11663a87fc22cb0a7b5 (MD5) Previous issue date: 2009-12-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research has had as objective of investigation: What opinions do teachers of Continued Teachers´ Education Group have about the use of HP-12C Calculator and Excel Spreadsheet to the teaching and learning of Financial Mathematics topics? The research has involved a practice accomplishment with, about, twenty Mathematics teachers (from Elementary and High School) of Alto Uruguai Region, in the north of RS, in which mathematical problems have been worked, involving concepts of Percentage, Simple and Compound Interest, using the Emulator of HP-12C ($12C++) Calculator and Excel Spreadsheet. The data have been collected from observations and instruments applied to teachers during the practice and have been organized in categories. The results have pointed out that teachers, in their opinions, consider HP-12C Calculator complex due to its programming language use, but they believe it is a resource that can help in the study of Percentage and Compound Interest, not being suggested to Simple Interest study. As for the Excel Spreadsheet use, the results have pointed out that it has resources to the classroom work like visualization, discussion and exploration that in people´s opinion, arouses students´ interest to the study of Financial Mathematics topics. / Este trabalho teve por objeto de investigação: Quais as opiniões que os professores de um Grupo de Formação Continuada têm a respeito do uso da Calculadora HP-12C e da Planilha Excel para o ensino e aprendizagem de tópicos de Matemática Financeira? A pesquisa envolveu a realização de uma prática com, aproximadamente, vinte professores de Matemática (do Ensino Fundamental e do Médio) da Região Alto Uruguai, no norte do RS, em que foram trabalhados problemas matemáticos, envolvendo conceitos de Porcentagem, Juros Simples e Compostos, utilizando-se o Emulador da Calculadora HP-12C ($12C++) e a Planilha Excel. Os dados foram coletados a partir de observações e de instrumentos aplicados aos professores, no decorrer da prática, e foram organizados em categorias. Os resultados destacaram que os professores, em suas opiniões, consideram complexa a Calculadora HP- 12C devido à linguagem de programação que utiliza, mas acreditam que é um recurso que pode auxiliar no estudo de Porcentagem e Juros Compostos, não sendo sugerido para o estudo de Juros Simples. Quanto ao uso da Planilha Excel, os resultados apontaram que a mesma possui recursos para o trabalho na sala de aula como visualização, discussão e exploração que, na opinião dos sujeitos, despertam o interesse dos alunos para o estudo de tópicos de Matemática Financeira.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-02-18T13:40:17Z No. of bitstreams: 1 leticiabotelhonatalino.pdf: 601168 bytes, checksum: 37a20d673fa9bc3f1454a7fc095febbe (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-02-26T13:30:28Z (GMT) No. of bitstreams: 1 leticiabotelhonatalino.pdf: 601168 bytes, checksum: 37a20d673fa9bc3f1454a7fc095febbe (MD5) / Made available in DSpace on 2016-02-26T13:30:28Z (GMT). No. of bitstreams: 1 leticiabotelhonatalino.pdf: 601168 bytes, checksum: 37a20d673fa9bc3f1454a7fc095febbe (MD5) Previous issue date: 2014-02-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho aborda o ensino da matemática financeira para alunos da EJA, educação de jovens e adultos, do ensino médio, visando contribuir com a revisão de conteúdos, como potências, porcentagem e introduzindo conceitos de logarítmo e progressões, além dos próprios conceitos envolvidos no referido conteúdo. A partir da observação não planejada, das dificuldades na retomada dos estudos e a defasagem de alguns conteúdos dos alunos da EJA, em salas que o autor lecionava foi sendo construída a ideia do tema da abordagem desse trabalho, resultando em quatro propostas de atividades de situações problemas relacionadas ao cotidiano de muitos desses alunos, onde a retomada de conceitos já aprendidos de matemática e a introdução de novos poderia ser feita concomitantemente a aplicação das atividades. Para tanto as propostas de atividades abordam situações cotidianas de parcelamento, financiamento, resgate de parcelas e uso da poupança, entre outras. Apesar da não aplicação das atividades pretende-se que ao se fazê-la os alunos tenham um ambiente propicio para compreender a importância e amplitude dos conteúdos abordados e aprender a aplica-los no seu dia-a-dia. / This paper discusses the teaching of financial mathematics for students of adult education high school in order to contribute to the review of content such as powers , percentage and introducing concepts of logarithm and progressions , beyond the actual concepts involved in that content. From unplanned observation of the difficulties in resuming studies and lag some contents of the EJA students in rooms that the author was teaching was being built theme idea of the approach of this work , resulting in four proposed activities of problem situations related to daily life of many of these students , where the resumption of math concepts already learned and the introduction of new could be done in addition to implementation of activities . For both the proposed activities address everyday situations installment , financing, redemption of shares and use of savings , among others . Despite the lack of implementation of activities is intended to make it up to the students to have a supportive environment to understand the importance and breadth of content covered and learn to apply them in their day -to-day .

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-04-05T16:56:00Z No. of bitstreams: 2 Dissertação - Adriano Rodrigues Teixeira - 2015.pdf: 12601586 bytes, checksum: 7d86470df655890876bcda71442e2d53 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-04-06T11:04:20Z (GMT) No. of bitstreams: 2 Dissertação - Adriano Rodrigues Teixeira - 2015.pdf: 12601586 bytes, checksum: 7d86470df655890876bcda71442e2d53 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-04-06T11:04:20Z (GMT). No. of bitstreams: 2 Dissertação - Adriano Rodrigues Teixeira - 2015.pdf: 12601586 bytes, checksum: 7d86470df655890876bcda71442e2d53 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-08-07 / The essay brings the main concepts of financial mathematics, looking to directly connect it to the events in our surroundings. As such, we descant about interest, discounting, periodic cycles and amortization systems. We will also apply Newtons method in order to determine the interest rates on payment series. / O trabalho traz os principais conceitos da matemática financeira, buscando sempre fazer uma ligação imediata com os acontecimentos ao nosso redor. A saber, discorremos sobre juros, descontos, séries periódicas e sistemas de amortizações. Além disso, aplicaremos o método de Newton para determinar da taxa de juros de séries de pagamentos.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2016-11-08T11:04:12Z No. of bitstreams: 2 Dissertação - Cláudia Ferreira Soares Alves - 2016.pdf: 1687196 bytes, checksum: 7930c5ab809fa83a42daa481c5cf866f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-11-08T17:45:12Z (GMT) No. of bitstreams: 2 Dissertação - Cláudia Ferreira Soares Alves - 2016.pdf: 1687196 bytes, checksum: 7930c5ab809fa83a42daa481c5cf866f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-11-08T17:45:12Z (GMT). No. of bitstreams: 2 Dissertação - Cláudia Ferreira Soares Alves - 2016.pdf: 1687196 bytes, checksum: 7930c5ab809fa83a42daa481c5cf866f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-09-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The research to which it refers aims to investigate how the Mathematical Modeling can collaborate in the teaching-learning student in financial mathematics topics, becoming the most dynamic and effective class. In the years of experience as a teacher, I could see the low stimulation of the students in learning math. Given this perception, and seeking alternatives that would alter this picture, and that math classes became more interesting, the idea of working with modeling. To achieve this goal we developed a study on this methodology, and an investigation directed using the perception of aspects involved in the teaching-learning process in Mathematical Modelling environment, based on studies of Biembengut and Barbosa. Before applying the methodology first, understand the model and modeling concepts, the application of the steps of the method according to these thinkers. We have seen the positive and negative aspects for the use of the technique; we also realize the importance of disseminating this methodology in the classroom in primary education using training courses for teachers. In order to investigate the contribution of the use of this methodology, we chose a model that motivate the student and befitted financial mathematics subject, they were encouraged to think in designing a floor plan and some parts of building your own home. The activities were designed and prepared for students to discuss financial mathematics topics. From this plant, the students had to calculate costs and financing of building materials as well as home and car loans. At the end of the survey, we noticed changes in the behavior of students, which have become more creative, critical, saw the importance of working in groups, and participated effectively in discussions. Moreover, with the research it was possible to find out a different way to develop the mathematical content, enabling greater interaction among students, through participation in the proposed activities, using the theory in practical situations of everyday life. / A pesquisa à qual se refere tem o objetivo de investigar o quanto a Modelagem Matemática pode colaborar no processo de ensino-aprendizagem do aluno em tópicos de matemática financeira, tornando a aula mais dinâmica e eficaz. Nos anos de experiência como professora pude notar o baixo estímulo dos alunos na aprendizagem de matemática. Diante dessa percepção, buscando alternativas que modificassem esse quadro e para que as aulas de matemática se tornassem mais interessantes, surgiu a ideia de trabalhar com Modelagem. Para alcançar esse objetivo foi desenvolvido um estudo sobre esta metodologia, além de uma investigação dirigida utilizando a percepção de aspectos envolvidos no processo de ensino-aprendizagem no ambiente de Modelagem Matemática, baseando-se nos estudos de Biembengut e Barbosa. Antes de aplicar a metodologia compreendemos primeiramente os conceitos de modelo e modelagem, etapas da aplicação da metodologia segundo os referidos pensadores. Vimos os aspectos positivos e negativos para a utilização da técnica, também percebemos a importância de se disseminar essa metodologia em sala de aula no ensino básico, utilizando cursos de capacitação para professores. Com o objetivo de verificar as contribuições da utilização da referida metodologia, escolhemos um modelo que motivasse o aluno e se adequasse ao assunto de matemática financeira, eles foram instigados a pensar na elaboração de uma planta baixa e algumas partes da construção de sua casa própria. As atividades foram pensadas e elaboradas para que os alunos discutissem tópicos de matemática financeira. Partindo desta planta, os alunos tiveram que calcular custos e financiamentos de materiais de construção e também financiamentos de casa e carro. Ao final da pesquisa, notamos as mudanças no comportamento dos discentes, os quais se tornaram mais criativos, críticos, viram a importância de se trabalhar em grupos e participaram de forma efetiva dos debates. Além disso, com a investigação foi possível averiguar um modo diferente de desenvolver o conteúdo matemático, viabilizando uma maior interação entre os alunos, por meio da participação nas atividades propostas, utilizando a teoria em situações práticas do dia a dia.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A situação financeira econômica atual vivida por nosso país nos faz refletir sobre a importância de estudarmos a Educação Financeira desde o ensino básico, a fim de instruirmos nossos jovens para que tenhamos um país saudável financeiramente. Neste trabalho, é abordado maneiras distintas de orientar nossos discentes do ensino médio sobre como investir, financiar e acima de tudo, conhecer os fundos de investimentos mais usados em nosso país. Familiarizados com estes fundos de investimentos, os jovens aprenderão como é importante economizar e investir. Métodos como aproximação linear de Newton ajudará aos jovens nos cálculos financeiros, bem como os colocarão perante uma ferramenta fundamental nesta área. O estudo sobre sistemas de amortizações auxiliará nossos jovens quanto aos financiamentos mais usados em nosso país, principalmente na aquisição do seu primeiro carro ou imóvel. A metodologia usada foi essencialmente uma pesquisa bibliográfica a partir da qual se consegue aprofundar no assunto pesquisado. A seguir, ajustou-se as hipóteses iniciais e delineou-se a estratégia concreta para o cumprimento dos objetivos propostos. Conclui-se que, com exercícios exemplos voltados para o cotidiano das pessoas, desperta-se um maior interesse pelos alunos em aprender a Matemática Financeira e aplicá-la em diversas situações de suas vidas. / Our motherlands current economic situation makes us reflect on the importance of studying the Financial Education since elementary school, so that we can educate our younger generation to make our country a healthier financially. This dissertation discusses many distinguished fashions for teaching high school students on how to invest, finance and, above all, getting them to know the investment funds that are used the most in our country. After being familiarized with these investment funds, the young students will learn the importance of saving and investing. Methods like Newtons linear approximation will help in their financial calculations, as well as making them acquainted with a fundamental tool for this field. The study of amortization systems will help students acknowledge our countrys most common financing choices, especially regarding the purchase of their first car or real estate. The methodology chosen for this dissertation was essentially a bibliographical research. In conclusion, with the help of examples and exercises with a focus on the daily life, there will be a greater interest among kids and teenagers in learning Financial Mathematics and its application in the most diverse situations.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A situação financeira econômica atual vivida por nosso país nos faz refletir sobre a importância de estudarmos a Educação Financeira desde o ensino básico, a fim de instruirmos nossos jovens para que tenhamos um país saudável financeiramente. Neste trabalho, é abordado maneiras distintas de orientar nossos discentes do ensino médio sobre como investir, financiar e acima de tudo, conhecer os fundos de investimentos mais usados em nosso país. Familiarizados com estes fundos de investimentos, os jovens aprenderão como é importante economizar e investir. Métodos como aproximação linear de Newton ajudará aos jovens nos cálculos financeiros, bem como os colocarão perante uma ferramenta fundamental nesta área. O estudo sobre sistemas de amortizações auxiliará nossos jovens quanto aos financiamentos mais usados em nosso país, principalmente na aquisição do seu primeiro carro ou imóvel. A metodologia usada foi essencialmente uma pesquisa bibliográfica a partir da qual se consegue aprofundar no assunto pesquisado. A seguir, ajustou-se as hipóteses iniciais e delineou-se a estratégia concreta para o cumprimento dos objetivos propostos. Conclui-se que, com exercícios exemplos voltados para o cotidiano das pessoas, desperta-se um maior interesse pelos alunos em aprender a Matemática Financeira e aplicá-la em diversas situações de suas vidas. / Our motherlands current economic situation makes us reflect on the importance of studying the Financial Education since elementary school, so that we can educate our younger generation to make our country a healthier financially. This dissertation discusses many distinguished fashions for teaching high school students on how to invest, finance and, above all, getting them to know the investment funds that are used the most in our country. After being familiarized with these investment funds, the young students will learn the importance of saving and investing. Methods like Newtons linear approximation will help in their financial calculations, as well as making them acquainted with a fundamental tool for this field. The study of amortization systems will help students acknowledge our countrys most common financing choices, especially regarding the purchase of their first car or real estate. The methodology chosen for this dissertation was essentially a bibliographical research. In conclusion, with the help of examples and exercises with a focus on the daily life, there will be a greater interest among kids and teenagers in learning Financial Mathematics and its application in the most diverse situations.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2017-06-23T18:21:37Z No. of bitstreams: 1 2016 - Gilmar de Paula Matta.pdf: 6703750 bytes, checksum: a15748db5b099e1dda229ecf947272eb (MD5) / Made available in DSpace on 2017-06-23T18:21:37Z (GMT). No. of bitstreams: 1 2016 - Gilmar de Paula Matta.pdf: 6703750 bytes, checksum: a15748db5b099e1dda229ecf947272eb (MD5) Previous issue date: 2016-03-18 / CAPES / The Financial Mathematics content covered in high school needs to be revised, it comes down to small applications that do not leave the school environment, does not apply to the daily lives of students. The purpose of this work is to integrate Financial Mathematics teaching content with what students need in their daily lives. For this activity have been developed that are results of a qualitative survey conducted in the city of Volta Redonda, RJ, with high school students from public and private schools. / O conte?do de Matem?tica Financeira abordado no Ensino M?dio precisa ser revisto, pois se resume a pequenas aplica??es que n?o saem do ambiente escolar, n?o se aplicando ao cotidiano dos alunos. A proposta deste trabalho ? integrar o conte?do do ensino de Matem?tica Financeira visto na escola, com o que, os alunos precisam no seu cotidiano. Para isso foram desenvolvidas atividades que s?o resultados de uma pesquisa qualitativa elaborada no munic?pio de Volta Redonda-RJ, com os alunos do Ensino M?dio da escola p?blica, Col?gio Get?lio Vargas e da escola particular, Col?gio Garra.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-04-13T19:29:25Z No. of bitstreams: 1 carloshenriquedasilvacavaca.pdf: 13890089 bytes, checksum: 21d2ffa22eccbd951ccbff944bdab00e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T03:23:29Z (GMT) No. of bitstreams: 1 carloshenriquedasilvacavaca.pdf: 13890089 bytes, checksum: 21d2ffa22eccbd951ccbff944bdab00e (MD5) / Made available in DSpace on 2016-04-24T03:23:29Z (GMT). No. of bitstreams: 1 carloshenriquedasilvacavaca.pdf: 13890089 bytes, checksum: 21d2ffa22eccbd951ccbff944bdab00e (MD5) Previous issue date: 2015-12-17 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho é o relato de uma pesquisa realizada com um grupo de alunos do segundo ano do ensino médio da EPCAR (Escola Preparatória de Cadetes do Ar) sobre o ensino de Matemática Financeira com o uso de problemas do cotidiano como estratégia de estímulo para tal aprendizado. Durante oito encontros com um grupo de dez alunos, ocorreu a seguinte ordem na abordagem da Matemática Financeira: apresentação dos conceitos, resolução de problemas simples e comuns encontrados nos livros didáticos e, finalmente, resolução de problemas levados à sala de aula, tirados, dentre outras fontes, de folheto de loja, constatando os valores informados em produtos vendidos à prestação, e também analisando criticamente esses valores. São estes problemas a principal razão desta pesquisa. Consideramos que os livros didáticos não exploram de modo consistente toda riqueza e proximidade da realidade que a Matemática Financeira oferece. Entendemos que o uso de folhetos de lojas que anunciam seus produtos, análise de boletos, consulta sobre empréstimos e aplicações financeiras, análise de financiamentos, são exemplos que podem e devem ser usados no ensino da Matemática Financeira por trazerem a realidade que qualquer cidadão vai se deparar em algum momento na trajetória da sua vida. Acreditamos que ao levar para sala de aula este tipo de situação há significante estímulo para o aprendizado da Matemática Financeira. Além disso, descobrimos ao longo da pesquisa a necessidade de se estabelecer um currículo comum na abordagem deste conteúdo para alunos do ensino médio, pois observamos que não há um consenso nos livros didáticos sobre até onde deve ser levado esse assunto. / This study is an account of a research carried out with a group of 16-year-old high school students in EPCAR (Preparatory School of Air Cadets) on Financial Mathematics teaching by means of using everyday mathematical problems as a stimulus strategy for such learning. Throughout eight meetings with a group of ten students, the following scenario took place regarding Financial Mathematics approach: presenting concepts; solving simple and common mathematical problems found in textbooks; and finally problems from other sources such as store flyers brought to classroom in which it was possible not only to notice the installment payment prices of goods as well as critically analyze them. These problems are the main reason of this research. We believe that textbooks do not approach consistently all the richness and reality Financial Mathematics is able to provide. We understand that the use of store flyers that advertise their products, the analysis of bills together with the examination of loans and investments, and the financing analysis, are examples which can and shall be used in Financial Mathematics teaching for they are capable of bringing the reality any citizen will face some time in his/ her life. We believe that by presenting the classroom this kind of activity there is a significant stimulus for learning Financial Mathematics. In addition, we have discovered during the research the need to set a common high school curriculum to focus this subject for we have observed that there is no consensus in textbooks about how far this content should be dealt with.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-12T17:23:39Z No. of bitstreams: 1 altamirobatistadarochajunior.pdf: 764525 bytes, checksum: 6494ccba37da04b473f97d9d1d9f8af3 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-27T19:33:07Z (GMT) No. of bitstreams: 1 altamirobatistadarochajunior.pdf: 764525 bytes, checksum: 6494ccba37da04b473f97d9d1d9f8af3 (MD5) / Made available in DSpace on 2016-06-27T19:33:07Z (GMT). No. of bitstreams: 1 altamirobatistadarochajunior.pdf: 764525 bytes, checksum: 6494ccba37da04b473f97d9d1d9f8af3 (MD5) Previous issue date: 2013-04-04 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho traz uma proposta de abordagem introdutória para o ensino de Matemática Financeira no ensino médio, que chamamos de Abordagem Cronol ógica, isto é, uma abordagem que valorize o correr natural do tempo, que analise etapa por etapa da evolução de uma dívida ou de um investimento. Desse modo podemos ter o aluno analisando o que realmente acontece per íodo a período, tirando conclusões e, assim, se tornando autônomo. Como embasamento teórico, buscamos pela história da Matemática justi cativas para as práticas usuais no mercado, principalmente as que aparentam ter culminado no surgimento do número e. / This paper proposes an introductory approach to Financial Math teaching in high-school, what we called Chronological Approach, that is, an approach that values the natural ow of time, which analyzes step by step the evolution of a debt or of an investment. This way, we can have the student analyzing what really happens in each period, drawing conclusions and, thus, becoming autonomous. As theoretical foundation, we looked through Mathematics History for explanations for the usual practices in the market, especially the ones that appears to have culminated in the emerging of the number e.

Probability theory is the study of random phenomena. Many dynamical systems with random influence, in nature or artificial complex systems, are better modeled by equations incorporating the intrinsic stochasticity involved. In probability theory, stochastic partial differential equations (SPDEs) generalize partial differential equations through random force terms and coefficients, while stochastic differential equations (SDEs) generalize ordinary differential equations. They are both abound in models involving Brownian motion throughout science, engineering and economics. However, Brownian motion is just one example of a random noisy input. The goal of this thesis is to make contributions in the study and applications of stochastic dynamical systems involving a wider variety of stochastic processes and noises. This is achieved by considering different models arising out of applications in thermal engineering, population dynamics and mathematical finance.<br><div><br></div><div>1. Power-type non-linearities in SDEs with rough noise: We consider a noisy differential equation driven by a rough noise that could be a fractional Brownian motion, a generalization of Brownian motion, while the equation's coefficient behaves like a power function. These coefficients are interesting because of their relation to classical population dynamics models, while their analysis is particularly challenging because of the intrinsic singularities. Two different methods are used to construct solutions: (i) In the one-dimensional case, a well-known transformation is used; (ii) For multidimensional situations, we find and quantify an improved regularity structure of the solution as it approaches the origin. Our research is the first successful analysis of the system described under a truly rough noise context. We find that the system is well-defined and yields non-unique solutions. In addition, the solutions possess the same roughness as that of the noise.<br></div><div><br></div><div>2. Parabolic Anderson model in rough environment: The parabolic Anderson model is one of the most interesting and challenging SPDEs used to model varied physical phenomena. Its original motivation involved bound states for electrons in crystals with impurities. It also provides a model for the growth of magnetic field in young stars and has an interpretation as a population growth model. The model can be expressed as a stochastic heat equation with additional multiplicative noise. This noise is traditionally a generalized derivative of Brownian motion. Here we consider a one dimensional parabolic Anderson model which is continuous in space and includes a more general rough noise. We first show that the equation admits a solution and that it is unique under some regularity assumptions on the initial condition. In addition, we show that it can be represented using the Feynman-Kac formula, thus providing a connection with the SPDE and a stochastic process, in this case a Brownian motion. The bulk of our study is devoted to explore the large time behavior of the solution, and we provide an explicit formula for the asymptotic behavior of the logarithm of the solution.<br></div><div><br></div><div>3. Heat conduction in semiconductors: Standard heat flow, at a macroscopic level, is modeled by the random erratic movements of Brownian motions starting at the source of heat. However, this diffusive nature of heat flow predicted by Brownian motion is not observed in certain materials (semiconductors, dielectric solids) over short length and time scales. The thermal transport in these materials is more akin to a super-diffusive heat flow, and necessitates the need for processes beyond Brownian motion to capture this heavy tailed behavior. In this context, we propose the use of a well-defined Lévy process, the so-called relativistic stable process to better model the observed phenomenon. This process captures the observed heat dynamics at short length-time scales and is also closely related to the relativistic Schrödinger operator. In addition, it serves as a good candidate for explaining the usual diffusive nature of heat flow under large length-time regimes. The goal is to verify our model against experimental data, retrieve the best parameters of the process and discuss their connections to material thermal properties.<br></div><div><br></div><div>4. Bond-pricing under partial information: We study an information asymmetry problem in a bond market. Especially we derive bond price dynamics of traders with different levels of information. We allow all information processes as well as the short rate to have jumps in their sample paths, thus representing more dramatic movements. In addition we allow the short rate to be modulated by all information processes in addition to having instantaneous feedbacks from the current levels of itself. A fully informed trader observes all information which affects the bond price while a partially informed trader observes only a part of it. We first obtain the bond price dynamic under the full information, and also derive the bond price of the partially informed trader using Bayesian filtering method. The key step is to perform a change of measure so that the dynamic under the new measure becomes computationally efficient.</div>