Orientador: Vera Lucia da Rocha Lopes / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T04:23:12Z (GMT). No. of bitstreams: 1 JimenezUrrea_Liliana_M.pdf: 3576733 bytes, checksum: 0e211564f3f081c060195cfa21aa4135 (MD5) Previous issue date: 2008 / Resumo: Neste trabalho apresentamos métodos de minimização irrestrita, de uma função objetivo F de várias variáveis, que não fazem uso nem do gradiente da função objetivo - métodos derivative-free, nem de aproximações do mesmo. Nosso objetivo básico foi estudar e comparar o desempenho de métodos desse tipo propostos por M. J. D. Powell, que consistem em aproximar a função F por funções quadráticas - modelos quadráticos - e minimizar tal aproximação em regiões de confiança. Além do algoritmo de Powell de 2002 - UOBYQA - são testados: uma variante dele, na qual utilizamos a escolha de alguns parâmetros, por nós estabelecida, e também a nova versão de NEWUOA, proposta por Powell em 2006. Todos os testes foram realizados com problemas da coleção de Hock-Schittkowski. São comparados os resultados numéricos obtidos pelos métodos de Powell: entre eles mesmos e também entre eles e um método de busca padrão de autoria de Virginia Torczon, o qual define, em cada iteração, um conjunto padrão de direções de busca a partir do ponto atual, procurando melhores valores para F. / Abstract: In this work we study numerical methods to solve problems of nonlinear programming without constraints, which do not make use, neither of the gradient of the objective function, nor of approaches to it. A method that consists on the approximation of the function F by a quadractic model, due to Powell (2002), UOBYQA, and a variant of this method were implemented. A new version of the NEWUOA, introduced by Powell in 2006, was also implemented. Besides the Powell algorithm, commentaries of the implementations are done. Numerical tests of such implementations with problems of the Hock-Schittkowski collection, are made at the end of the work. There are also comparisons of the Powell methods among themselves, and also a comparison among the Powell methods with a pattern search method, which looks for the improvement of the value of the objective function throughout a set of directions, depending on the current point. Such a method is due to Virginia Torczon. / Mestrado / Otimização / Mestre em Matemática Aplicada

Esta dissertação revisa a literatura acadêmica existente sobre a teoria de opções utilizando os modelos de precificação com saltos. Os conceitos foram equalizados, a nomenclatura foi padronizada, sendo gerado um material de referência sobre o assunto. O pressuposto de lognormalidade com volatilidade constante não é aceito pelo mercado financeiro. É freqüente, no meio acadêmico, a busca de modelos que reproduzam os fenômenos observados de leptocurtose ou assimetria dos log-retornos financeiros e que possuam a mesma robustez e facilidade para manipulação analítica do consagrado modelo de Black-Scholes. Os modelos com saltos são uma alternativa para esse problema. Avaliou-se o modelo de Kou no mercado acionário brasileiro composto por um componente de difusão que segue um movimento browniano geométrico e um componente de saltos que segue um processo de Poisson com intensidade do salto descrito por uma distribuição duplamente exponencial. A simulação histórica do modelo aponta, em geral, uma superioridade preditiva do modelo, porém as dificuldades de calibração dos parâmetros e de hedge em mercados incompletos são as principais deficiências para o uso dos modelos com saltos. / This master dissertation reviews the academic literature about option pricing and hedging with jumps. The theory was equalized and the notation was standardized, becoming this document a reference document about this subject. The log-normality with constant volatility is not accepted by the market. Academics search consistent models with the same analytical capabilities like Black-Scholes? model which can support the observed leptokurtosis or asymmetry of the financial daily log-returns behavior. The jump models are an alternative to these issues. The Kou?s model was evaluated and this one consists of two parts: the first part being continuous and following a geometric Brownian motion and the second being a jump process with its jump intensity defined by a double exponential distribution. The model backtesting showed a better predictive performance of the Kou´s model against other models. However, there are some handicaps regarding to the parameters calibration and hedging.

Orientadores: Margarida Pinheiro Mello, Maria Aparecida Diniz Ehrhardt / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-22T15:49:27Z (GMT). No. of bitstreams: 1 Ferreira_DaianeGoncalves_M.pdf: 1441315 bytes, checksum: 1196d8b21c6254dbdd0e0d68266fa707 (MD5) Previous issue date: 2013 / Resumo: Métodos de Otimização de terceira ordem, embora de longa tradição, eram considerados, até passado recente, impraticáveis, devido à taxa com que o esforço computacional cresce em função da dimensão do problema. Avanços no desenvolvimento de estruturas de dados, rotinas que trabalham com estas estruturas e a exploração da esparsidade de grande parte dos problemas encontrados na prática já permitem implementações destes métodos que podem torná-los competitivos com métodos de segunda ordem. O objeto desta dissertação é a apresentação do método de Halley, um método de terceira ordem, sua implementação em MATLAB e a realização de testes computacionais, visando uma comparação empírica de sua eficiência frente ao método de Newton, o método de segunda ordem mais empregado na atualidade / Abstract: Higher order optimization methods, though of long-standing tradition, until recently have been deemed impractical, due to the rate of increase of the computational effort as a function of the size of the problem. Advances in the development of data structures, routines that work with these structures and the use of the sparsity of a vast range of practical problems have led to implementations of these methods that are competitive with second order methods. The object of this dissertation is the study of Halley's method, a thirdorder method, the development of a MATLAB implementation thereof and its testing, aiming at an empirical comparison of its efficiency against that of Newton's method, the second-order method most widely used today / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

Purpose: The purpose of the study was to investigate how companies are affected by currency hedging in international trade. One purpose was to investigate and identify the type of currency risks companies are most exposed to and what currency hedging methods are used to handle these. Methodology: To answer the study's question, research was conducted by using a qualitative data method and a content analysis method. Theoretical framework: The focus has been on these theories; Modigliani and Miller theory, currency risk management and previous studies. Result: The result of the study consists of a presentation of the processed data as underlies the analysis being carried out. Conclusion: The study found that the currency exposures which companies are primarily exposed to in international trade are transaction and translation exposures. Of the eight companies investigated in the study, seven of them focused on transaction exposure. The study also indicates that the most commonly used derivative instruments used by companies are futures, options and swaps, where futures due to its flexibility came first, options on the second place and swaps on the third place. The most important and used purchase currencies that the companies deal with are Euro, British pound and US-dollars. Whether it is profitable for companies to hedge their currency risks or not, this study found that currency hedging is profitable for companies. / Syfte: Syftet med studien var att undersöka hur företagen påverkas av valutasäkring vid internationell handel. Ett delsyfte var att undersöka och kartlägga vilken typ av valutarisk företagen är mest exponerade för samt vilka valutasäkringsmetoder som används vid hantering av dessa. Metod: För att besvara studiens frågeställning genomfördes forskningen genom en kvalitativ metod och en innehållsanalysmetod. Teoretiskt perspektiv: Fokus har legat på dessa teorier; Modigliani & Millers teori, valutariskhantering och tidigare studier. Empiri: Empirin innefattar den bearbetade datan som har samlats in från respektive företag samt är grunden för studiens analys. Slutsats: Studien kom fram till att den valutaexponering som företagen främst utsätts för vid internationell handel var transaktions-och omräkningsexponering. Av de åtta företag som har undersökts i studien visade sig att sju av dessa fokuserade på transaktionsexponering. Studien visade även att de vanligaste derivatinstrumenten som används av företagen var terminer, optioner och swappar. Terminer på grund av dess flexibilitet kom på första plats, optioner på andra plats och swappar på tredje plats. De viktigaste och mest använda inköpsvalutorna som företagen handlar med var euro, brittiskt pund och amerikanska dollar. Huruvida det är lönsamt för företagen att valutasäkra eller inte, tydde denna studies fynd på att valutasäkring är lönsamt för företag.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Ebastine is a second generation antihistaminic clinically used for the treatment of allergic rhinitis and chronic urticaria. Pseudoephedrine hydrochloride is a direct- and indirectacting sympathomimetic, commonly combined with other drugs for their decongestant effect. In Brazil, this drugs association is available in capsules. In the literature, as well as in the official compendium, there are no methods for simultaneous analysis of ebastine and pseudoephedrine hydrochloride in pharmaceutical formulations. In the present work, liquid chromatography (HPLC) and derivative spectrophotometry (UVD) methods were developed and validated for quantification of this drugs association, in capsules. The HPLC analysis were performed on a C18 column, using a mobile phase composed of methanol: acetonitrile: ammonium acetate buffer pH 6.8 (85:5:15, v/v), run at a flow rate of 1,0 mL.min-1, with UV detection at 254 nm. In the UVD method, ebastine was quantified in the first derivative (dA/dλ), at 263.5 and 252.8 nm, respectively. All of them were validated in the following parameters: linearity, precision and accuracy. The specificity was evaluated in the HPLC assay by stress testing. The methods showed good linarity (r>0.99), precision (RSD<2%) and accuracy; the results, statistically compared, did not show significant difference (p>0,05). / A ebastina é um fármaco anti-histamínico de segunda geração utilizado clinicamente no tratamento da rinite alérgica e urticária crônica. O cloridrato de pseudoefedrina é um agente simpaticomimético de ação direta e indireta, muito utilizado em associação com outros fármacos pelo seu efeito descongestionante. No mercado brasileiro, encontra-se a associação desses dois fármacos disponível na forma de cápsulas. Na literatura, bem como em compêndios oficiais, não são descritos métodos para análise simultânea de ebastina e cloridrato de pseudoefedrina em formulações farmacêuticas. No presente trabalho, métodos por cromatografia líquida de alta eficiência (CLAE) e por espectrofotometria derivada (UVD) foram desenvolvidos e validados para quantificação simultânea desses fármacos, em cápsulas. As análises por CLAE foram realizadas em coluna C18, utilizando fase móvel composta de metanol: acetonitrila: tampão acetato de amônio pH 6,8 (80:5:15, v/v), eluída isocraticamente a 1,0 mL.min-1, com detecção UV em 254 nm. No método por UVD, a ebastina e o cloridrato de pseudoefedrina foram quantificados na primeira derivada (dA/dλ), em 263,5 e 252,8 nm, respectivamente. Ambos os métodos foram validados frente aos parâmetros de linearidade, precisão e exatidão. A especificidade do método por CLAE foi avaliada através do teste de estresse. Os métodos mostraram boa linearidade (r>0,99), precisão (DPR<2%) e exatidão. Os resultados obtidos por CLAE e UVD foram comparados estatisticamente e não apresentaram diferença significativa (p>0,05).

Action filed by Company Member Diploma thesis Action filed by Company Member is focused on analysis of the problematic areas concerning action by a member followed by a suggestion of possible solutions to such issues. The thesis is also focused on alternative mechanisms inside the company and consideration concerning the (non-)usage of the institute in practice. The first chapter defines the nature and objectives of the action by a member. Subsequently concrete types of occurrence are briefly defined and the institute is put into historic connection with the rules stated in Act No. 513/1991 Coll., the Commercial Code. The second chapter focuses on analysis of the main problematic areas of the institute. The thesis focuses on problems concerning active legitimation and its consequences when it is lost during the proceedings. Chapter also deals with the issues concerning representation of the company during the proceedings and the loss of the right to represent the company. The duty to pay judicial fees and expenses of the legal representation (attorney's expenses) or the issues concerning limitation period are also important. The chapter discusses the influence of the reflective loss, which is stated in Section 213 of the Act No. 89/2012 Coll., the Civil Code. The third chapter deals with the...

We develop expansion methods as a new computational approach towards high-dimensional partial differential equations (PDEs), particularly of such type as arising in the valuation of financial derivatives. The proposed methods are extended from [41] and use principal component analysis (PCA) of the underlying process in combination with a Taylor expansion of the value function into solutions to low-dimensional PDEs. They enable calculation of highly accurate approximate solutions with computational complexity polynomial in the number of dimensions for PDEs with a low number of dominant principal components. For the case of PDEs with constant coefficients, we show existence of expansion solutions and prove theoretical error bounds. We give a precise characterisation of when our methods can be applied and construct specific examples of a first and second order version. We provide numerical results showing that the empirically observed convergence speeds are in agreement with the theoretical predictions. For the case of PDEs with varying coefficients, we give a heuristic motivation using the Parametrix approach and empirically test the methods' accuracy for a range of variable parameter stock models. We demonstrate the applicability of our expansion methods to real-world securities pricing problems by considering path-dependent and early-exercise options in the LIBOR market model. Using the example of Bermudan swaptions and Ratchet floors, which are considered difficult benchmark problems, we give a careful analysis of the numerical accuracy and computational complexity. We are able to demonstrate that for problems with medium to high dimensionality, around 60-100, and moderate time horizons, the presented PDE methods deliver results comparable in accuracy to benchmark state-of-the-art Monte Carlo methods in similar or (significantly) faster run time.

This dissertation evaluates development of exchange rates and its specific effects on STAP company a.s. The aim of this paper is to present the events that have had influence on the development of the exchange rate between Euro and Czech Crown and precautionary measures taken by STAP a.s. to prevent related risks. The first part comprises a summary of events that had a significant impact on the exchange rate development; the risks created by these events and methods devised to prevent these risks. The second part evaluates the specific financial derivatives used by STAP a.s. and their impact. Finally the recommendation is made for the future more effective usage of the financial instruments.

Orientador: Maria Aparecida Diniz Ehrhardt / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação / Made available in DSpace on 2018-08-22T06:10:21Z (GMT). No. of bitstreams: 1 Ferreira_DeiseGoncalves_M.pdf: 2631020 bytes, checksum: 45eb84901394375843735b1fdef599ad (MD5) Previous issue date: 2013 / Resumo: Neste trabalho voltamos nossa atenção para métodos de otimização que não fazem uso de derivadas. Dentre esses, estamos interessadas em um método de busca padrão para minimização de funções com restrições lineares. Abordamos um algoritmo proposto por Lewis e Torczon, cuja ideia geral é que o padrão deve conter direções de busca ao longo das quais iterações factíveis sejam determinadas. O algoritmo possui resultados de convergência global. Realizamos sua implementação computacional, e propomos novas estratégias de busca e atualização do tamanho do passo, além de um novo padrão de direções de busca. Realizamos testes numéricos, de modo a analisar o desempenho das estratégias propostas e comparar o desempenho do padrão de direções que introduzimos com o proposto por Lewis e Torczon / Abstract: In this work, our interest lies on derivative-free optimization methods. Among these, our aim is to study a pattern search method for linearly constrained minimization. We studied an algorithm proposed by Lewis and Torsion, whose general idea is that the pattern must contain search directions in which feasible iterations must be computed. The algorithm has global convergence results. We accomplished its computational implementation and we propose new strategies of search and updating rule for the step-length control parameter. We also propose a new pattern of search directions. We accomplished numerical experiments in order to analyze the performance of our proposals and also to compare the performance of our pattern with the one proposed by Lewis and Torczon / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

We deal with locally ill-posed nonlinear operator equations F(x) = y in L^2(0,1), where the Fréchet derivatives A = F'(x_0) of the nonlinear forward operator F are compact linear integral operators A = M ◦ J with a multiplication operator M with integrable multiplier function m and with the simple integration operator J. In particular, we give examples of nonlinear inverse problems in natural sciences and stochastic finance that can be written in such a form with linearizations that contain multiplication operators. Moreover, we consider the corresponding ill-posed linear operator equations Ax = y and their degree of ill-posedness. In particular, we discuss the fact that the noncompact multiplication operator M has only a restricted influence on this degree of ill-posedness even if m has essential zeros of various order.