Die vorliegende Arbeit beschäftigt sich mit verschiedenen Aspekten der Finanzmathematik. Ein erweitertes Libor Markt Modell wird betrachtet, welches genug Flexibilität bietet, um akkurat an Caplets und Swaptions zu kalibrieren. Weiterhin wird die Bewertung komplexerer Finanzderivate, zum Beispiel durch Simulation, behandelt. In hohen Dimensionen können solche Simulationen sehr zeitaufwendig sein. Es werden mögliche Verbesserungen bezüglich der Komplexität aufgezeigt, z.B. durch Faktorreduktion. Zusätzlich wird das sogenannte Andersen-Simulationsschema von einer auf mehrere Dimensionen erweitert, wobei das Konzept des „Momentmatchings“ zur Approximation des Volaprozesses in einem Heston Modell genutzt wird. Die daraus resultierende verbesserten Konvergenz des Gesamtprozesses führt zu einer verringerten Komplexität. Des Weiteren wird die Bewertung Amerikanischer Optionen als optimales Stoppproblem betrachtet. In höheren Dimensionen ist die simulationsbasierte Bewertung meist die einzig praktikable Lösung, da diese eine dimensionsunabhängige Konvergenz gewährleistet. Eine neue Methode der Varianzreduktion, die Multilevel-Idee, wird hier angewandt. Es wird eine untere Preisschranke unter zu Hilfenahme der Methode der „policy iteration“ hergeleitet. Dafür werden Konvergenzraten für die Simulation des Optionspreises erarbeitet und eine detaillierte Komplexitätsanalyse dargestellt. Abschließend wird das Preisen von Amerikanischen Optionen unter Modellunsicherheit behandelt, wodurch die Restriktion, nur ein bestimmtes Wahrscheinlichkeitsmodell zu betrachten, entfällt. Verschiedene Modelle können plausibel sein und zu verschiedenen Optionswerten führen. Dieser Ansatz führt zu einem nichtlinearen, verallgemeinerten Erwartungsfunktional. Mit Hilfe einer verallgemeinerte Snell''sche Einhüllende wird das Bellman Prinzip hergeleitet. Dadurch kann eine Lösung durch Rückwärtsrekursion erhalten werden. Ein numerischer Algorithmus liefert untere und obere Preisschranken. / The work presented here deals with several aspects of financial mathematics. An extended Libor market model is considered offering enough flexibility to accurately calibrate to various market data for caplets and swaptions. Moreover the evaluation of more complex financial derivatives is considered, for instance by simulation. In high dimension such simulations can be very time consuming. Possible improvements regarding the complexity of the simulation are shown, e.g. factor reduction. In addition the well known Andersen simulation scheme is extended from one to multiple dimensions using the concept of moment matching for the approximation of the vola process in a Heston model. This results in an improved convergence of the whole process thus yielding a reduced complexity. Further the problem of evaluating so called American options as optimal stopping problem is considered. For an efficient evaluation of these options, particularly in high dimensions, a simulation based approach offering dimension independent convergence often happens to be the only practicable solution. A new method of variance reduction given by the multilevel idea is applied to this approach. A lower bound for the option price is obtained using “multilevel policy iteration” method. Convergence rates for the simulation of the option price are obtained and a detailed complexity analysis is presented. Finally the valuation of American options under model uncertainty is examined. This lifts the restriction of considering one particular probabilistic model only. Different models might be plausible and may lead to different option values. This approach leads to a non-linear expectation functional, calling for a generalization of the standard expectation case. A generalized Snell envelope is obtained, enabling a backward recursion via Bellman principle. A numerical algorithm to valuate American options under ambiguity provides lower and upper price bounds.

Submitted by Alzir Antônio Mahl (alzir_mahl@hotmail.com) on 2017-05-10T11:54:36Z No. of bitstreams: 1 ALZIR ANTONIO MAHL_Impressão.pdf: 14048608 bytes, checksum: 9be7df17ffa2c77f8b1b9025cc96badd (MD5) / Approved for entry into archive by Maria Auxiliadora da Silva Lopes (silopes@ufba.br) on 2017-05-10T14:52:49Z (GMT) No. of bitstreams: 1 ALZIR ANTONIO MAHL_Impressão.pdf: 14048608 bytes, checksum: 9be7df17ffa2c77f8b1b9025cc96badd (MD5) / Made available in DSpace on 2017-05-10T14:52:49Z (GMT). No. of bitstreams: 1 ALZIR ANTONIO MAHL_Impressão.pdf: 14048608 bytes, checksum: 9be7df17ffa2c77f8b1b9025cc96badd (MD5) / A pesquisa buscou avaliar a evolução dos sistemas regionais de inovação no Brasil no período 2000 a 2011. Foram analisados os sistemas de inovação de 13 (treze) estados selecionados das cinco macrorregiões do Brasil, considerando para tanto: se as empresas empregaram conhecimento tecnológico nas atividades de inovação; se a produção e difusão do conhecimento tecnológico são elementos que melhoram o desempenho de um sistema regional de inovação; se é possível caracterizar estes sistemas regionais de inovação a partir das informações sobre as inovações das empresas e; se a maturidade dos SRIs pode ser avaliada por meio de variáveis relacionadas com as atividades de inovação. Para tanto, utilizaram-se as informações relatadas nas atividades de inovação pelas empresas na PINTEC destes estados como variável proxy para representar os sistemas regionais. Realizou-se uma revisão bibliográfica sobre conceitos relacionados ao trabalho, como conhecimento tecnológico, sistema de inovação e sistema regional de inovação, bem como discutiu-se o tema das políticas multinível ou mix de políticas, que podem ser, por exemplo, a combinação das políticas industrial e de inovação. Ademais, utilizaram-se os estados como unidades de análise dos SRIs, pelo fato destes possuírem os ingredientes necessários para caracterização dos sistemas regionais de inovação. A metodologia da pesquisa foi baseada na análise multivariada de dados, na qual os dados capturados das empresas participantes da pesquisa PINTEC dos anos de 2000, 2003, 2005, 2008 e 2011, foram agrupadas em variáveis onde aplicou-se a técnica da análise fatorial. Esta técnica permitiu a redução das 46 variáveis iniciais para uma matriz 13x67 (treze variáveis e sessenta e sete observações), o que permitiu a análise dos 13 SRIs a partir da obtenção de três fatores após a análise fatorial, denominados de Produção de Conhecimentos, Impactos e Obstáculos. No período da pesquisa, verificou-se a evolução dos SRIs em geral, pelo aumento da produção de conhecimentos e dos impactos das inovações, bem como da diminuição dos obstáculos às atividades de inovação das empresas. Como resultado, foi realizada uma análise das correlações entre os três fatores e indicadores de desenvolvimento socioeconômico (PIB per capita, Índice de Gini e Produtividade do Trabalho na Indústria) para os trezes SRIs. A definição de um indicador de correlação permitiu classificar os estados quanto à correlação entre as atividades de inovação e o desenvolvimento socioeconômico, resultando na formação de quatro grupos de estados, a saber: estados com correlação mais forte, moderada, média e fraca. / ABSTRACT The research aimed to evaluate the development of regional innovation systems in Brazil from 2000 to 2011. The innovation systems of thirteen selected states from the five macro regions of Brazil were analyzed considering: if companies used technological knowledge in innovation activities; if the production and dissemination of technological knowledge improve the performance of a regional innovation system; if it is possible to characterize these regional innovation systems from the information on the companies’ innovations and; if the maturity of SRIs can be evaluated by means of variables related to innovation activities. The information reported during innovation activities by the PINTEC companies in these states were used as a proxy variable to represent the regional systems. A literature review was conducted on concepts related to work, such as technological knowledge, innovation system and regional innovation system as well as the issue of multilevel policies or policy mix, which can be, for example, the combination of industrial and innovation policies. Moreover, the states were used as units of analysis of SRIs, because they have the necessary ingredients to characterize the regional innovation systems. The research methodology was based on multivariate data analysis, in which the captured data of the participating companies on PINTEC research from the years 2000, 2003, 2005, 2008 and 2011 were grouped into variables, where the technique of factor analysis was applied. This technique allowed the reduction of the 46 initial variables for a 13x67 matrix (thirteen variables and sixty-seven observations), which allowed the analysis of 13 SRIs from the achievement of three factors after the factor analysis, named Knowledge Production, Impacts and Obstacles. During the survey, it was possible to notice the evolution of SRIs in general, by the increase of knowledge production and the impact of innovation, as well as the reduction of barriers to the companies innovation activities. As a result, an analysis of correlations between the three factors and socio-economic development indicators (GDP per capita, Gini Index and Labor Productivity in Industry) was held for the thirteen SRIs. The definition of a correlation indicator allowed to classify the states about the correlation between innovation activity and socioeconomic development, resulting in the formation of four groups of states: states with stronger, moderate, medium and weak correlation.