Title: Option Pricing Author: Radek Moravec Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathematical Statistics In the present thesis we deal with European call option pricing using lattice approaches. We introduce a discrete market model and show a way how to find an arbitrage price of financial instruments on complete markets. It's equal to the discounted value of future expected cash flow. We present the binomial option pricing model and generalize it into multinomial model. We test the resulting formula on real market data obtained from NYSE and NASDAQ. We suggest a parameter estimate method which is based on time series of historical observations of daily close price. We compare calculated option prices with their real market value and try to explain the reasons of the differences. 1

The thesis studies nonlinear nonparametric models used in time series analy- sis. It gives basic introduction to the time series and states different nonlinear nonparametric models including their estimates. Special attention is paid to three of them, CHARN, FAR and AFAR model. Their properties and esti- mation techniques are presented. We also show techniques that select values of the parametres used further in estimation methods. The properties of time series models are investigated in simulation and real data studies. 1

Title: Application of hp-adaptive discontinuous Galerkin method to com- pressible flow simulation Author: Karol Tarčák Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vít Dolejší, Ph.D., DSc. Abstract: In the present work we study an residuum estimate of disconti- nuous Galerkin method for the solution of Navier-Stokes equations. Firstly we summarize the construction of the viscous compressible flow model via Navier-Stokes partial differential equation and discontinuous Galerkin met- hod. Then we propose an extension of an already known residuum estimate for stationary problems to non-stationary problems. We observe the beha- vior of the proposed estimate and modify an existing hp-adaptive algorithm to use our estimate. Finally we apply the modified algorithm on test cases and present adapted meshes from the numerical experiments. Keywords: discontinuous Galerkin method, adaptivity, error estimate 4

Adaptive methods in finite element analysis are essential tools in the efficient computation and error control of problems that may exhibit singularities. In this paper, we consider solving a boundary value problem which exhibits a singularity at the origin due to both the structure of the domain and the regularity of the exact solution. We introduce a hybrid mixed finite element method using Lagrange Multipliers to initially solve the partial differential equation for the both the flux and displacement. An a posteriori error estimate is then applied both locally and globally to approximate the error in the computed flux with that of the exact flux. Local estimation is the key tool in identifying where the mesh should be refined so that the error in the computed flux is controlled while maintaining efficiency in computation. Finally, we introduce a simple refinement process in order to improve the accuracy in the computed solutions. Numerical experiments are conducted to support the advantages of mesh refinement over a fixed uniform mesh.

Este trabalho teve por objetivo determinar a influência das características dos países e indústrias no comércio intra-industrial brasileiro de produtos manufaturados, considerando fluxos de quantidades comercializadas ao ano, para o período de 2002 a 2006, através de estimativas de uma equação gravitacional adaptada à análise dessa forma de comércio. As variáveis explicativas são relacionadas ao tamanho de mercado, representado pela proxy LPIBij, diferenças entre as rendas per capita dos países, representadas pela proxy LdPIBpcij, e tarifas aduaneiras aplicadas pelos países importadores, LTarifas. Tais variáveis foram utilizadas para analisar o comércio intraindustrial e seus componentes horizontal e vertical. A fundamentação teórica para proceder à segmentação do comércio intra-industrial brasileiro, segundo tais características, foi derivada de trabalhos conduzidos por Falvey (1981), Helpman e Krugman, (1985) e Greenaway, et al. (1995). A mensuração do Índice de Grubel-Lloyd e a posterior separação dos componentes do CII utilizando valor unitário indicam uma composição do comércio intra-industrial brasileiro com forte predomínio do componente CII Vertical Inferior.Os resultados da estimação das equações gravitacionais, com a utilização dos dados em painel e a utilização de Poisson Pseudo-Maximum-Likelihood comprovou ser a mais adequada para a estimativa econométrica.Para o comércio intraindustrial total, os resultados indicaram que o tamanho de mercado, tem um efeito positivo sobre o fluxo de exportação dos produtos brasileiros com comércio intraindustrial (0,517), porém, as diferenças entre as rendas per capita dos países (-0,183) e tarifas aduaneiras dos países importadores (-0,356), são negativamente relacionados. Os resultados para o comércio intra-industrial vertical e horizontal apresentam os mesmos sinais que o CII total, com alteração na magnitude. / This study aimed to determine the influence of characteristics for countries and industries in intra-industry trade (IIT) of Brazilian manufactured products, considering the annual trade flows for the period 2002 to 2006 and using a gravity equation adapted to analysis this form of trade . The explanatory variables are related to market size, represented by proxy LPIBij, differences between per capita incomes of countries represented by proxy LdPIBpcij, and tariffs imposed by importing countries, represented by proxy LTarifas. These variables were used to analyze the intra-industry trade and its horizontal and vertical components. The theoretical basis to make the segmentation of intra-industry in Brazil, according to such characteristics, was derived from studies conducted by Falvey (1981), Helpman and Krugman (1985) and Greenaway et al.(1995). The measurement of the Grubel-Lloyd index and the subsequent separation of components from IIT using unit value indicates that the brazilian intra-industry trade has a strong predominance of IIT Vertical Low quality. The results of the estimation of the gravitational equations with the use of panel data and the use of Poisson Pseudo- Maximum-Likelihood proved to be the most suitable for econometric estimation. The results for intra-industry total indicated that the market size, has a positive effect on the flow of exports of Brazilian products with intra-industry trade (0,517), however, the differences between per capita incomes (-0,183) of countries and tariffs in importing countries (-0,356) have a negative relation. The results for vertical and horizontal intraindustry trade have the same signals than intra-industry total but they differ in magnitude.

O presente trabalho teve como objetivo estimar as populações canina e felina domiciliadas nos distritos administrativos do município de São Paulo, caracterizando-as demograficamente, bem como o oferecimento de cuidados veterinários e a forma de manutenção dos animais em domicílio. Para tal, utilizou-se amostragem complexa com seleção aleatória em dois estágios: setores censitários e domicílios. Em cada distrito administrativo, foram visitados seis setores censitários e 20 domicílios em cada setor sorteado. De setembro de 2006 a setembro de 2009, um total de 11.272 entrevistas foram feitas. A média de cão/domicílio com cão foi estimada em 1,60 e a média de gato/domicílio com gato, 1,69. A razão homem:cão foi estimada em 4,34 e a razão homem:gato, 19,33. A partir da população humana de 10.882.121 habitantes, no ano de 2007, estimou-se a população animal em 2.507.401 cães e 562.965 gatos. A população canina é composta de 52,7% de machos, enquanto a felina, de 45,1%. A proporção de felinos castrados (39,0%) foi superior a dos caninos (17,1%), considerando ambos os gêneros. As proporções de fêmeas esterilizadas (23,4% dentre os cães e 46,1% dentre os gatos) são superiores às de machos (11,4% dentre os cães e 31,5% dentre os gatos), em ambas as espécies. A idade média de cães foi estimada em 4,99 anos e a de gatos, 3,53 anos. A proporção de gatos não vacinados contra a raiva nos últimos 12 meses (6,8%) foi superior à proporção de cães (1,6%). A proporção de cães com restrição de acesso à rua (64,4%) foi superior à dos gatos (42,5%). A restrição e a esterilização dos animais são reflexos da posse responsável que deve ser incessantemente discutida e divulgada a fim de promover conscientização dos proprietários quanto aos modos de manutenção e oferecimento de cuidados veterinários. A caracterização das populações animais é a base da estruturação de progamas de controle populacional e de zoonoses. Estudos populacionais que respeitam a heterogeinedade dos aspectos administrativos e geográficos de um município, permitem medidas de ações em saúde mais direcionadas. / The present work aimed at estimate the owned dog and cat populations at the administrative districts of São Paulo city, in terms of its demography, but also the veterinary care and maintenance of animals. To achieve this goal, a complex sample with random selection in two stages (censitary sectors and households) was used. Six censitary sectors in each administrative district and 20 households in each sampled sector were visited. From September 2006 to September 2009, 11.272 interviews were made. The dog per household with dogs average was 1.60 and the cat per household with cats average was 1.69. The human:dog ratio was 4.34 and the human:cat ratio was 19.33. Since the human population was 10,882,121, in 2007, the dog population was estimated in 2,507,401 and the cat population in 562,965. The dog population was composted of 52.7% males, while among the cat population was 45.1%. The proportion of both male and female sterilized cats (39,0%) was higher than dogs (17.1%). The proportion of sterilized females (23.4% among dogs and 46.1% among cats) was higher than males (11.4% among dogs and 31.5% among cats) in both species. The mean age of dogs was 4.99 years as for cats, 3.53 years. The proportion of cats non-vaccinated against rabies (6.8%) was higher than dogs (1.6%) in the last 12 months. The proportion of restricted (access to the street) dogs (64.4%) was higher than restricted cats (42.5%). The animal restriction and sterilization are effects of responsible ownership and must be constantly discussed and disseminated to improve owners awareness about the way of maintaining and providing veterinary care to dogs and cats. The characterization of canine and feline populations is essential to structure an animal population management programme and zoonosis control. Population studies must respect the heterogeneity of administrative and geographical aspects of a municipality in order to provide more focused measures of public health.

To help address the knowledge gap between science and practice this study explores the possible positive benefits of using a more pedagogical effect size estimate when presenting statistical relationships. Traditional presentation has shown limitations with major downsides being that scientific findings are misinterpreted or misunderstood even by professionals. This study explores the possible effects of the non-traditional effect size estimate Common Language Effect Size (CLES) on different training outcomes for HR professionals. This study also explores the possible effect of cognitive system preference on training outcomes. Results show no overall effect of CLES on either training outcomes or cognitive system. A positive effect of CLES on training outcome is found at the subfactor level showing a significant effect. The results can be interpreted that non-traditional effect size estimates have a limited effect on training outcomes. This small but valuable piece to bridge the gap of knowledge is discussed.

"The fragmented environment in the construction industry has a big influence on production. The multi-disciplinary nature of the project development process imposes the need for clear communications and team effort coordination. Information Technology (IT) has been playing a tremendous role in facilitating this process. The most recent contribution of IT in this regard is the Building Information Model (BIM). It is clear that BIM technology improves the design drawings productivity; drawings are automatically coordinated in all views from plans, to sections, to elevations, to details and to perspectives. It also provides an innovative way of scheduling through by allowing a 3D visualization of the construction progress. But, there are still many technical issues that still need to be addressed before this technology is fully adopted by the industry. For example, what are the files formats that BIM supports? What is the needed knowledge for best use of BIM? How does BIM integrate with the estimating discipline? Where does BIM store the building data? What are the codes that are shown in the automatically generated “quantity take-offs” schedules? This research attempts to provide answers to these questions and explores possible ways to link different coding systems within the BIM platform itself. After reviewing the basic design concepts from the conceptual to the construction stages and how it is related to the different project delivery ways, this work illustrates the role of different work breakdown structures (WBS) in the life cycle of estimating discipline from the preliminary to the detailed stage. The research reviewed the different database designs and structures, the database management systems (DBMS), as well as the database organization systems. This review draws a picture on how information system (IS) and its tools support the different needs of the multiple players involved in a construction project. The focus was on the object oriented database and building information model (BIM) software, and how it integrates with other estimating and project planning software. The findings seem promising, but before BIM technology can reshape the construction industry, it is still necessary to conduct additional experimental work as the software continues to evolve and becomes mature."

Algoritmos de detecção de linhas são usados em muitos campos de aplicação, tais como visão computacional e automação como base para análises mais complexas. Por exemplo, a informação de linha pode ser usada como dado de entrada para algoritmos de detecção de objetos ou mesmo para a estimativa da orientação espacial de robôs aéreos. Uma das formas de detectar linhas é através do uso de um processo de filtragem não linear chamado deWide Line Detector (WLD). Esse algoritmo é eficaz na marcação de pixels de linha em imagens em tons de cinza, separando linhas claras ou linhas escuras. Contudo, os algoritmos de detecção de linha não estão normalmente preocupados com a estimativa de largura local individual associada a um pixel. Se disponível, tal informação poderia ser explorada por algoritmos de visão computacional. Além do mais, a informação de cor também é extensivamente usada em visão computacional como um discriminante de objetos, mas o WLD não a usa. Neste Trabalho, nós propusemos a extensão do WLD para imagens em cores. Nós também desenvolvemos um novo kernel monotonicamente crescente que é mais eficiente e mais robusto para detectar linhas do que que os kernels monotonicamente decrescentes usados pelo WLD. Por fim, desenvolvemos uma maneira de obter uma estimativa de largura de linha partindo da densidade local associada a similaridade entre pixels, revertendo o processo usado pelo WLD para estimar qual kernel deve ser usado. Diversos experimentos foram realizados com o método proposto considerando diferentes parâmetros, além da comparação com o WLD tradicional, para analizar a eficácia do método. / Line detection algorithms are used by many application fields, such as computer vision and automation, as a basis for more complex analysis. For instance, line information can be used as input to object detection algorithms or even attitude estimation in flying robots. One way to detect lines is to use an isotropic nonlinear filtering procedure called the Wide Line Detector (WLD). This algorithm is effective to highlight the line pixels in gray scale images, separating dark or bright lines. However, line detection algorithms are not normally concerned with the pixel-wise estimation of thickness. If available, such information could be further explored by computer vision algorithms. Furthermore, color is extensively used in computer vision as an object discriminant, but not by the WLD. In this work, we propose the extension of the WLD to color images. We also develop a method that allows the estimation of the line width locally using only the density information and no border or center line information. Finally, we develop a new monotonically increasing kernel that is more efficient and yet effective to detect lines than the monotonically decreasing kernels used by the WLD. Finally, we devise a way ro obtain the wideline thickness from the density estimate obtained from the similarity between pixels, reverting the process used by the WLD to determine which kernel should be used. We perform several experiments with the proposed method, considering different parameters, and comparing it to the traditional WLD algorithm to assess the effectiveness of the method.

Cette these se compose de quatre chapîtres et une annexe. Le premier chapître est consacre à des idées fondamentales de la theorie du flot de Ricci, qui montre comment nos travaux sont reliés a l'histoire entière. Dans le deuxième chapître, nous construisons une solution du flot de Ricci sur une variete a symétrie de rotation de telle sorte qu'il reste un collecteur complet a l'heure maximale. Nous dérivons également le non-effondrement pour certaines solutions anciennes à proximité de leur temps maximal. Chacun de ces deux resultats sont liés à la régularité des limites des solutions. Dans le troisième chapître, nous montrons qu'une estimation de type Shi d'ordre un est valable pour tenseur de Ricci sur des variétés qui satisfont l'inégalité Bianchi faibles. Le dernier chapître s'interesse aux gradient solitons de Ricci qui sont en expansion. Nous discutons du problème de classification et montrons que chaque cône tangent à l'infini d'un soliton expansion à "fast-than-quadratic-decay" courbure doit être $mathbb{R}^n$. / This thesis consists of four chapters and an appendix. The first chapter is dedicated to the fundamental ideas of the theory of Ricci flow, which shows how our works are connected to the whole story. In the second chapter, we construct a solution of Ricci flow on a rotationally symmetric manifold such that it remains a complete manifold at the maximal time. We also derive a noncollapsing property for certain ancient solutions near their maximal times. Both of these two results are related to the regularity of limits of solutions. In the third chapter, we show that a first order Shi-type estimate holds for Ricci tensor on manifolds which satisfy the weak Bianchi inequality. The last chapter is concerned with expanding gradient Ricci solitons. There we discuss the classification problem and show that every tangent cone at infinity of an expanding soliton with fast-than-quadratic-decay curvature must be $mathbb{R}^n$.