My PhD thesis concentrates on the field of stochastic analysis, with focus on stochastic optimization and applications in finance. It is composed of two parts: the first part studies an optimal stopping problem, and the second part studies an optimal control problem. The first topic considers a one-dimensional transient and downwards drifting diffusion process X, and detects the optimal times of a random time(denoted as ρ). In particular, we consider two classes of random times: (1) the last time when the process exits a certain level l; (2) the time when the process reaches its maximum. For each random time, we solve the optimization problem infτ E[λ(τ- ρ)+ +(1-λ)(ρ - τ)+] overall all stopping times. For the last exit time, the process should stop optimally when it runs below some fixed level k the first time, where k is the solution of an explicit defined equation. For the ultimate maximum time, the process should stop optimally when it runs below a boundary which is the maximal positive solution (if exists) of a first-order ordinary differential equation which lies below the line λs for all s > 0 . The second topic solves an optimal consumption and investment problem for a risk-averse investor who is sensitive to declines than to increases of standard living (i.e., the investor is loss averse), and the investment opportunities are constant. We use the tools of stochastic control and duality methods to solve the resulting free-boundary problem in an infinite time horizon. Briefly, the investor consumes constantly when holding a moderate amount of wealth. In bliss time, the investor increases the consumption so that the consumption-wealth ratio reaches some fixed minimum level; in gloom time, the investor decreases the consumption gradually. Moreover, high loss aversion tends to raise the consumption-wealth ratio, but cut the investment-wealth ratio overall.

There were about 6.7 % of inhabitants in foreclosure in the Czech Republic in 2020. The most likely cause is population's low financial literacy whose bases we get at primary school. So we asked whether pupils really learn financial literacy at primary school. We found data for teaching plan in the framework educational programme. We realised, using a questionnaire for teachers, among other things that the number of lessons dedicated to financial literacy is really low. We verified fulfilment of framework educational programme by a test for primary school pupils which was completed by 113 pupils. It showed that they have very low knowledge of financial literacy. Then, we evaluated the situation after primary school through the same test which was filled in by 157 people who completed primary school. The results were better than in case of pupils. Finally, we suggested steps for increasing financial literacy, for instance raising the number of lessons. 1

In this research project, we introduced an agent-based banking system based on systematic trust. The features of the model and attributes of the agents are defined and analyzed precisely, and the results are explained. Some of this model's features include but are not limited to considering the savings system, insurance deposits, the impact of the Central Bank loans, and correlated regional shocks in a banking system. Different Scenarios are applied. The results indicate that by having the Central Bank loans in the model, the banking system experience dramatically fewer failures. Even if some correlated regional shocks occur, the system can be more stable than when the Central Bank does not exist. Moreover, the trust system establishes and forms during different financial periods based on the bank's clients’ point of view about the bank's performance as an intelligent system to attract more capital for the system by providing some information for the agents to join the more prestigious banks. Conclusively, in the early financial periods, banks need more financial supports to support the clients’ deposits and to make their reputation for attracting more clients; hence the Central Bank is an essential parameter to help the banks to be more stable and supports the banks in their early stages of growth. The Central Bank loans would be significantly important in panic times, such as regional correlated preference shocks. / Thesis / Master of Science (MSc)

This thesis is a comparative study where the question is whether a neural network approach can outperform the principal component analysis (PCA) approach for predicting changes of interest rate curves. Today PCA is the industry standard model for predicting interest rate curves. Specifically the goal is to better understand the correlation structure between Swedish and European swap rates. The disadvantage with the PCA approach is that only the information contained in the covariance matrix can be used and not for example whether or not the curve might behave different depending on the current state. In other words, some information that might be quite important to the curve dynamic is lost in the PCA approach. This raises the question whether the lost information is important for prediction accuracy or not. As previously been shown by Alexei Kondratyev in the paper "Learning Curve Dynamics with Artificial Neural Networks", the neural network approach is able to use more information in the data and therefore has potential to outperform the PCA approach. Our thesis shows that the neural network approach is able to achieve the same or higher accuracy than PCA when performing long term predictions. The results show that the neural network model has potential to replace the PCA model, however, it is a more time consuming model. Higher accuracy can probably be achieved if the network is more optimized. / Det här är en jämförande studie där syftet är att undersöka hurvida noggrannare prediktioner kan uppnås genom att använda sig av artificiella neurala nätverk (ANN) istället för principalkomponentanalys (PCA) för att förutspå swapräntekurvor. PCA är idag industristandard för att förutspå räntekurvor. Specifikt är målet att bättre kunna förstå korrelationsstrukturen mellan de Svenska swapräntorna och de Europiska swapräntorna. En nackdel med PCA är att den enda tillgängliga informationen sparas i kovariansmatrisen. Det kan till exempel vara fallet att kurvan beter sig väldigt annorlunda beroende på om de nuvarande räntenivåerna är höga eller låga. Eftersom att sådan information går förlorad i PCA-modellen ligger intresset i att undersöka hur mycket noggrannare prediktionerna kan bli om man tar tillvara på ännu mer av informationen i datan. Som Alexei Kondratyev visar i rapporten "Learning Curve Dynamics with Artificial Neural Networks", så har ANN-modellen potential att ersätta PCA-modellen för att förutspå räntekurvor. I denna studie framgår det att ANN-modellen uppnår samma eller bättre resultat jämfört med PCA-modellen vid längre prediktioner.

In today's society sustainability has become an important subject and has an impact on various sectors. Corporations include sustainability in their corporate strategy, which further affects the field of corporate finance. This has lead to a new insight among investors to include a sustainability criterion in their investment processes. This research has investigated how Investor AB could optimize their portfolio by including sustainability criterion (ESG) and how different portfolio setups will differ from each other.  The research has been conducted utilizing Markowitz portfolio optimization described by Markowitz theory. The application of the theory has been extended with a third criterion of a weighted ESG score rating where the optimal solutions were found using the notion of Pareto optimality and quadratic programming. Different cases have been created to find how more sustainable portfolios can differ from each other. The research shows that portfolios consisting of companies with higher ESG rating do not significantly decrease the expected return but can suffer from higher standard deviation, which indicates that it is driven by assets with higher ESG score rating. The obtained results show that the portfolios obtained including the third criterion will not always obtain a value of Jensen's Alpha above zero (0) and are therefore not optimal strategies to outperform the benchmark index, SIX Return Index. A portfolio that consists of non-sustainable and sustainable assets has performed better than other portfolios that under- or overperform from the perspective of sustainability.  The conclusion is that an investor must sacrifice a higher weighted ESG score rating of its portfolio to obtain a higher expected return and less risk. An investor that aims for higher return, must exclude the sustainability criterion. / I dagens samhälle har hållbarhet blivit ett aktuellt ämne inom olika affärsverksamheter. Bolag beaktar hållbarhet i delar av sin dagliga verksamhet vilket påverkar bolagets finansiella ställning. Med tiden har investerare fått upp ögonen för hållbara investeringar. Denna studie har till syfte att undersöka hur Investor AB kan optimera sin portfölj genom att inkludera kriterierna för miljö, samhälle/social och bolagsstyrning (ESG). Vidare har studien till syfte att undersöka hur framtagning enligt olika portföljer kan skilja sig åt.  Undersökningen har genomförts med hjälp av Markowitz teori om portföljoptimering. Tillämpningen av teorin har utvidgats med ett tredje ESG kriterium i optimeringsproblemet baserat på teorin om Pareto-optimala lösningar och optimeringslära. Olika portföljer har skapats för att undersöka hur mer hållbara portföljer skiljer sig från varandra. Studien visar att bolag med krav på högre ESG ranking i en portfölj inte kommer att minska förväntade avkastningen, däremot kommer standardavvikelsen att öka. Genom att optimera sin avkastning och samtidigt ta hänsyn till en portföljs hållbarhet har det visats sig i portföljutvecklingen att det inte är möjligt att nå högre avkastning än jämförelse indexet, SIX Return Index.  Slutsatsen är att investare riskerar andra preferenser såsom avkastning i de fall de ska inkludera en ytterliggare hållbarhetsfaktor i sin investeringsprocess. Investor ABs portfölj bygger dock sin förväntade avkastning på dem mer hållbara bolagen eftersom förväntad avkastning inte minskar avsevärt när ett hållbarhetskriterium inkluderas. Om en investerare önskar en högre avkastning bör de inte inkluder en hållbarhetskriterium.

Made available in DSpace on 2017-07-21T20:56:32Z (GMT). No. of bitstreams: 1 Rafael Guilherme Gallas.pdf: 1511477 bytes, checksum: 928ab6607f276f89ee3d1860bf417aad (MD5) Previous issue date: 2013-04-05 / The Mathematics Finance have great importance for the high school student, it is in this stage of life that this student enters the work force and start using cash more often. Therefore, this study aims to reinforce the importance of teaching students of Mathematics Finance at the high school, as well as the benefits of its correct use in adulthood. Initially we reviewed the official guidelines such as: PCN, PCNEM and Curricular Guidelines regarding Mathematics Finance later we analyzed some of the textbooks that are used in state schools of the State of Parana to verify if they are in accordance with the guidelines set out in official documents. We propose to review the main concepts of Mathematics Finance used in high school and to developed an activity involving its main concepts. This activity aims to approach the Mathematics Finance in a easier form, based mainly on examples and materials that are close to the students like grocery flyers, involving the social context in which they are inserted as a way to encourage their study and a consequent class improvement , with a possible reduction of class detachment / A Matemática Financeira possui grande importância para o aluno do ensino médio, pois é nesta etapa da vida que este aluno ingressa no mercado de trabalho e começa a utilizar o dinheiro com mais frequência. Sendo assim, este trabalho tem como objetivo reforçar aos alunos a importância do ensino da Matemática Financeira no ensino médio, bem como os benefícios de sua correta utilização na vida adulta. Inicialmente verifica-se o que orientam os documentos oficiais como: PCN, PCNEM e Diretrizes Curriculares a respeito da Matemática Financeira, e a partir disto analisamos alguns dos livros didáticos que são utilizados na rede estadual de ensino do Estado do Paraná para verificar se estão de acordo com as diretrizes previstas nos documentos oficiais. Propôs-se uma revisão dos principais conceitos de Matemática Financeira usados no ensino médio e após isso desenvolveu-se uma proposta de atividade envolvendo seus principais conceitos. Nesta atividade propõe-se a abordagem da Matemática Financeira de uma maneira simplificada, fundamentada principalmente em exemplos e materiais que chegam até os alunos, como panfletos de supermercado, envolvendo o contexto social em que este está inserido, como forma de incentivar o seu estudo e a consequente melhoria das aulas, com uma possível redução no desinteresse das aulas.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-08-28T18:37:11Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) MATEMÁTICA FINANCEIRA - SIMÃO PEDRO.pdf: 1350923 bytes, checksum: 9fac353769529f3c26c61ace9663f875 (MD5) / Made available in DSpace on 2014-08-28T18:37:11Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) MATEMÁTICA FINANCEIRA - SIMÃO PEDRO.pdf: 1350923 bytes, checksum: 9fac353769529f3c26c61ace9663f875 (MD5) Previous issue date: 2013-04-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The goal of this work is to serve as a guide so that teachers can orientate and enrich their pedagogical practice in an appropriate manner as well as to enable readers to solve problems of their daily lives, such as: evaluating loans, understand and decide on investments, among other similar. With this, emphasize the importance of processing your teaching and learning. We believe that this is a matter of great importance in the daily lives of people, especially after the stabilization of the Brazilian economy because the real plan, where people now have easier access to credit, acquiring Financing and loans with higher frequency. This justi es a solid learning and future application of Financial Mathematics. Through their study, students can be prepared to perform commercial and nancial transactions that occur in your daily life, such as choosing the best form of payment, cash or term, analyzing investment alternatives, understand the functioning of nancial markets organize your personal nances etc. / O objetivo deste trabalho é servir de guia para que os professores possam orientar e enriquecer sua prática pedagógica de maneira adequada, além de capacitar o leitor para resolver problemas do cotidiano, tais como: avaliar empréstimos, entender e optar sobre investimentos, dentre outros semelhantes. Com isto, destacar a importância de se processar o seu ensino e aprendizagem. Consideramos que esse é um assunto de grande relevância no dia a dia das pessoas , principalmente, após a estabilização da economia brasileira em virtude do plano real, onde as pessoas passaram a ter acesso facilitado a linhas de crédito, adquirindo financiamentos e empréstimos com maior freqüência. Isso justi ca uma sólida aprendizagem e futura aplicação da Matemática Financeira. Por meio de seu estudo, o leitor pode ser preparado para realizar transações comerciais e financeiras que ocorrem no seu dia a dia, como optar pela melhor forma de pagamento, à vista ou a prazo, analisar alternativas de investimentos, entender o funcionamento do mercado fi nanceiro, organizar suas fi nanças pessoais etc.

The work deals with financial mathematics and its teaching in upper secondary school. This thesis contains introduction to finance, simple and compound in- terest, securities, bonds, loans and savings. The work is also presented in the form of web pages. The web pages are enhanced with interactive features such as applets in GeoGebra and step-by-step solutions for exercises. The web pages include a final test in which one can check his knowledge. The test contains ten randomly generated tasks which cover the curriculum of the thesis. The work is meant as an extending teaching materials for upper secondary school pupils. 1

Jump diffusion models are being used more and more often in financial applications. Consisting of a Brownian motion (with drift) and a jump component, such models have a number of parameters that have to be set at some level. Maximum Likelihood Estimation (MLE) turns out to be suitable for this task, however it is computationally demanding. For a complicated likelihood function it is seldom possible to find derivatives. The global maximum of a likelihood function defined for a jump diffusion model can however, be obtained by numerical methods. I chose to use the Bound Optimization BY Quadratic Approximation (BOBYQA) method which happened to be effective in this case. However, results of Maximum Likelihood Estimation (MLE) proved to be hard to interpret.

The paper deals with the problem of finding an optimal one-time rebalancing strategy for the Bachelier model, and makes some remarks for the similar problem within Black-Scholes model. The problem is studied on finite time interval under mean-square criterion of optimality. The methods of the paper are based on the results for optimal stopping problem and standard mean-square criterion. The solution of the problem, considered in the paper, let us interpret how and - that is more important for us -when investor should rebalance the portfolio, if he wants to hedge it in the best way.