This thesis presents the prediction algorithm for the price of the share of risky asset. The price of the share is presented by dynamic model and observation is presented by the measurement model. Dynamic model is derived by using Stochastic Calculus. The algorithm is simulated by using Matlab.

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Submitted by Onia Arantes Albuquerque (onia.ufg@gmail.com) on 2018-10-30T12:22:27Z No. of bitstreams: 2 Dissertação - Jair Elias Amim Júnior - 2018.pdf: 5510530 bytes, checksum: 7fcf54ff9710ae2bbf014c158ab7152a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Rejected by Luciana Ferreira (lucgeral@gmail.com), reason: O subtítulo em inglês deve começar em minúsculo. A citação está com problema : Dissertação (Mestrado em Matemática em Rede Nacional - Sociedade Brasileira de Matemática) ERRADO (Mestrado em Matemática em Rede Nacional) CERTO on 2018-10-30T13:39:00Z (GMT) / Submitted by Onia Arantes Albuquerque (onia.ufg@gmail.com) on 2018-10-30T13:51:12Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Jair Elias Amim Júnior - 2018.pdf: 5510530 bytes, checksum: 7fcf54ff9710ae2bbf014c158ab7152a (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-10-30T15:16:29Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Jair Elias Amim Júnior - 2018.pdf: 5510530 bytes, checksum: 7fcf54ff9710ae2bbf014c158ab7152a (MD5) / Made available in DSpace on 2018-10-30T15:16:29Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Jair Elias Amim Júnior - 2018.pdf: 5510530 bytes, checksum: 7fcf54ff9710ae2bbf014c158ab7152a (MD5) Previous issue date: 2018-10-05 / The present work was a technical report that introduced the course and the results of the investigate work accomplished in the Professional Mathematics Master’s Program in National Network (Profmat). I proposed a method of teaching Financial Mathematics focused in the use of financial applications for smartphone, having as main objective to verify the students' development in relation to the made decisions in situations that are offered to them the possibility to choose the applications to assist in the resolution of problems. As main benchmark was used the heuristics of problem solving proposed by George Polya (1995), the use of smartphones and Applications as Pedagogic tools, according to Voltolini (2016) and Soares (2016): the creating of a virtual learning environmoent, according to Shitsuka (2012), and the critic mathematics education associated with resolution of problem, according to Skovsmose (2000). From the application of the method it resulted an electronic textbook of studies as education product, whose title is "Financial Mathematical with Use of Applications for Smartphone." Aimed for teachers of the Basic Education, the electronic textbook has theoretical summaries and links for the resolutions of the exercises in videos posted on YouTube. A qualitative research was carried out in four meetings, and the instruments of data collection were questionnaires, record sheets and videos captured by the participating students themselves. This allowed to observe the capacity of the students' autonomy in the choice of the applications. The critical glance that they developed when analyzing interest rates and options of payments, serves with foundation for the construction of a financial education to be used in daily routine. / O presente trabalho tratou de um Relatório Técnico que apresentou o percurso e os resultados do trabalho investigativo realizado no Programa de Mestrado Profissional em Matemática em Rede Nacional (Profmat). Propus um método de ensino de Matemática Financeira focado no uso de aplicativos financeiros para smartphone, tendo como objetivo principal verificar o desenvolvimento dos alunos em relação à tomada de decisões em situações nas quais lhes são oferecidas a possibilidade de escolha de aplicativos para auxiliar na resolução de problemas. Os principais referenciais foram a heurística de resolução de problemas proposta por George Polya (1995); o uso de smartphones e aplicativos como ferramentas pedagógicas, segundo Voltolini (2016) e Soares (2016); a criação de um ambiente virtual de aprendizagem, segundo Shitsuka (2012) e a educação matemática crítica associada à resolução de problemas, segundo Skovsmose (2000). Da aplicação do método resultou uma apostila eletrônica como Produto Educacional, cujo título é “Matemática Financeira com uso de aplicativos para Smartphone. Destinada a professores do Ensino Básico, a apostila conta com resumos teóricos e links para as resoluções dos exercícios em vídeos postados no meu canal no YouTube. Foi realizada uma pesquisa qualitativa em quatro encontros, sendo que os instrumentos de coletas de dados foram questionários, folhas de registros e vídeos capturados pelos próprios alunos participantes. Isto permitiu observar a capacidade de autonomia dos alunos na escolha dos aplicativos e o desenvolvimento do olhar crítico ao analisar taxas de juros e opções de pagamentos, servindo como alicerce para a construção de uma educação financeira a ser usada no dia a dia.

Many important tasks in finance often rely on complex and time-consuming computations. The rapid development of quantum technology has raised the question of whether quantum computing can be used to solve these tasks more efficiently than classical computing. This thesis studies the potential use of quantum computing in finance by solving differently-sized problem instances of the mean-variance portfolio selection model using commercially available quantum resources. The experiments employ gate-based quantum computers and quantum annealing, the two main technologies for realizing a quantum computer. To solve the mean-variance optimization problem on gate-based quantum computers, the model was formulated as a quadratic unconstrained binary optimization (QUBO) problem, which was then used as input to quantum resources available on the largest quantum computing as a service (QCaaS) platforms, IBM Quantum Lab, Microsoft Azure Quantum and Amazon Braket. To solve the problem using quantum annealing, a hybrid quantum-classical solver available on the service D-Wave Leap was employed, which takes as input the mean-variance model’s constrained quadratic form. The problem instances were also solved classically on the model’s QUBO form, where the results acted as benchmarks for the performances of the quantum resources. The results were evaluated based on three performance metrics: time-to-solve, solution quality, and cost-to-solve. The findings indicate that gate-based quantum computers are not yet mature enough to consistently find optimal solutions, with the computation times being long and costly as well. Moreover, the use of gate-based quantum computers was not trouble-free, with the majority of quantum computers failing to even complete the jobs. Quantum annealing, on the other hand, demonstrated greater maturity, with the hybrid solver being capable of fast and accurate optimization, even for very large problem instances. The results from using the hybrid solver justify further research into quantum annealing, to better understand the capabilities and limitations of the technology. The results also indicate that quantum annealing has reached a level of maturity where it has the potential to make a significant impact on financial institutions, creating value that cannot be obtained by using classical computing.

Artificial intelligence, AI, has received increasing attention from the finance industry over recent years. There have been many successful applications of AI in finance, including but not limited to derivative pricing, asset management, credit risk, algorithmic trading, and simulation of time series with stylized facts. This thesis introduces various applications of AI in two major fields, namely (a) quantitative/computational finance and (b) asset management. In each chapter, we address non-stationarity of markets under consideration and focus on building methodologies that would work under the non-stationary behavior of those market. In computational finance, fast and accurate algorithms are of great importance, especially when analytical solutions are unavailable. Although traditional methods are reliable and easily explainable, they are computationally expensive. Transform methods like Fast-Fourier transform provide faster option pricing, yet they cannot be applied to path-dependent products. In Chapter 2, we build a pricing engine based on supervised deep neural networks. We show that neural networks can replicate major stochastic processes with or without stochastic volatility in both pure diffusion and pure jump frameworks. We validate our models across different ranges of model parameters. Supervised neural networks accelerate the derivative pricing significantly compared to traditional methods. Applications of AI in asset management are triggered by different dynamics, but they are fully data-driven and thus rely on the availability of data. Chapter 3 proposes a novel prediction framework for cash flow forecasting of illiquid products/assets. Our single-step neural network model provides the investors and managers of funds with a tool to manage the liquidity of their cash flows for financial planning. Our framework is also sensitive to adverse market conditions that could help prepare for upcoming crises such as Covid. In Chapter 4, we propose novel methodologies for mergers and acquisitions (M&A) to predict the deal announcement based on rumors and takeover success. M&A data is highly imbalanced in nature, and the cost of misclassifying a cancelled rumor/cancelled deal as announced deal/takeover success is higher than the other. Hence, we utilize sequential model-based optimization with tree-parzen estimators to maximize the recall score by tuning hyperparameters of neural networks. We improve the recall by 10% without sacrificing accuracy, and our results show that the proposed methodology is robust against changing market environments. In the last chapter, we build a two-step neural network model for sector rotation strategies using macroeconomic variables. The portfolio built based on our proposed model not only beats the benchmark portfolio but can also predict longer horizons.

The main aim of my thesis on the topic of "Euler's number in mathematical analysis" is to create an overview of the Euler numbers in calculus. This essay in the first part deals with the rise of the number e, in other parts of the current use of calculus. Purpose of this work is the insight students of secondary schools and universities to problems Euler numbers and to better understand the importance of e not only in mathematics.