Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2005. / Extremes are unusual or rare events. However, when such events – for example earthquakes, tidal waves and market crashes - do take place, they typically cause enormous losses, both in terms of human lives and monetary value. For this reason, it is of critical importance to accurately model extremal events. Extreme value theory entails the development of statistical models and techniques in order to describe and model such rare observations. In this document we discuss aspects of extreme value theory. This theory consists of two approaches: The classical maxima method, based on the properties of the maximum of a sample and the more popular threshold theory, based upon the properties of exceedances of a specified threshold value. This document provides the practitioner with the theoretical and practical tools for both these approaches. This will enable him/her to perform extreme value analyses with confidence. Extreme value theory – for both approaches - is based upon asymptotic arguments. For finite samples, the limiting result for the sample maximum holds approximately only. Similarly, for finite choices of the threshold, the limiting distribution for exceedances of that threshold holds only approximately. In this document we investigate the quality of extreme value based inferences with regard to the unknown underlying distribution when the sample size or threshold is finite. Estimation of extreme tail quantiles of the underlying distribution, as well as the calculation of confidence intervals, are typically the most important objectives of an extreme analysis. For that reason, we evaluate the accuracy of extreme based inferences in terms of these estimates. This investigation was carried out using a simulation study, performed with the software package S-Plus.

With extensive use of information systems in day-to-day business operations, many organizations are facing challenges to develop robust computer-based information systems that are secure and widely used by the user community. In order to develop information systems that are secure and useful, understanding what stakeholders consider important and value about the security and usability is critical. Security refers to confidentiality, integrity and availability and usability refers to efficiency, effectiveness and user satisfaction. Using Value Focused Thinking approach, this research first proposes the usability objectives based on the values of system developers and users. Using the security objectives proposed by Dhillon & Torkzadeh (2006) and the usability objectives, this research proposes hierarchies with the overall/over-arching goals of security (confidentiality, integrity, availability) and/or usability (efficiency, effectiveness and satisfaction). This research also analyzes a case of computer hacking and identifies which of the security and usability objectives that have not been met in that case study. The research contributions which include the usability objectives and security and usability hierarchies can be useful for theoretical as well as practical purposes.

Nuclear energy is a source of carbon free power. With many countries striving to make deep carbon cuts in their energy sectors, nuclear energy could be a large part of the solution. One of the main obstacles standing in the way of the use of nuclear energy is the issue of used nuclear fuel disposal. According to the NEI, the U.S. creates about 2000 metric tons of used nuclear fuel per year and has generated around 76,000 metric tons of used nuclear fuel over the last 4 decades. While there are technical problems that need to be solved, it is primarily the public and political opposition to the disposal of used nuclear fuel that stands in the way of progress in this area. This work addresses this issue through Multi-Criteria Decision Analysis (MCDA). To make a decision among ten different fuel cycles, we have brought together five stakeholders: Nuclear Scientists and Engineers, Environmental Scientists, Economists, Political Scientists, and The General Public. Using Multi-Attribute Value Theory (MAVT), we have been able to develop decision models for each stakeholder as well as a model that combines them all and came to the conclusion that of the ten fuel cycles considered, the best decision is to continue to use On Site Dry Cask Storage. This decision is made with small sample sizes but the methodology could be applied at much larger scales and can potentially be used to choose a fuel cycle that encounters much less political and social opposition to its implementation.

The central issue of this thesis is investigating the eventuality of systemic break- downs in the international financial system through examining systemic depen- dence between bank and insurance sectors. Standard models of systemic risk often use correlation of stock returns to evaluate the magnitude of intercon- nectedness between financial institutions. One of the main drawbacks of this approach is that it is oriented towards observations occurring along the central part of the distribution and it does not capture the dependence structure of outlying observations. To account for that, we use methodology which builds on the Extreme Value Theory and is solely focused on capturing dependence in extremes. The analysis is performed using the data on stock prices of the EU largest banks and insurance companies. We study dependencies in the pre- crisis and post-crisis period. The objective is to discover which sector poses a higher systemic threat to the international financial stability. Also, we try to find empirical evidence about an increase in interconnections in recent post- crisis years. We find that in both examined periods systemic dependence in the banking sector is higher than in the insurance sector. Our results also in- dicate that extremal interconnections in the respective sectors increased,...

[pt] A partir da década de 90, a metodologia de Valor em Risco (VaR) se difundiu pelo mundo, tanto em instituições financeiras quanto em não financeiras, como uma boa prática de mensuração de riscos. Um dos fatos estilizados mais pronunciados acerca das distribuições de retornos financeiros diz respeito à presença de caudas pesadas. Isso torna os modelos paramétricos tradicionais de cálculo de Valor em Risco (VaR) inadequados para a estimação de VaR de baixas probabilidades, dado que estes se baseiam na hipótese de normalidade para as distribuições dos retornos. Sendo assim, o objetivo do presente trabalho é investigar o desempenho de modelos baseados na Teoria dos Valores Extremos para o cálculo do VaR. Os resultados indicam que os modelos baseados na Teoria dos Valores Extremos são adequados para a modelagem das caudas, e consequentemente para a estimação de Valor em Risco quando os níveis de probabilidade de interesse são baixos. / [en] Since the 90 decade, the use of Value at Risk (VaR) methodology has been disseminated among both financial and non-financial institutions around the world, as a good practice in terms of risks management. The existence of fat tails is one of the striking stylized facts of financial returns distributions. This fact makes the use of traditional parametric models for Value at Risk (VaR) estimation unsuitable for the estimation of low probability events. This is because traditional models are based on the conditional normality assumption for financial returns distributions. The main purpose of this dissertation is to investigate the performance of VaR models based on Extreme Value Theory. The results indicates that Extreme Value Theory based models are suitable for low probability VaR estimation.

Hipóteses precisas são características naturais das teorias econômicas de determinação do valor ou preço de ativos financeiros. Nessas teorias, a precisão das hipóteses assume a forma do conceito de equilíbrio ou da não arbitragem. Esse último possui um papel fundamental nas teorias de finanças. Sob certas condições, o Teorema Fundamental do Apreçamento de Ativos estabelece um sistema único e coerente para valorização dos ativos em mercados não arbitrados, valendo-se para tal das formulações para processos de martingal. A análise da distribuição estatística desses ativos financeiros ajuda no entendimento de como os participantes se comportam nos mercados, gerando assim as condições para se arbitrar. Nesse sentido, a tese defendida é a de que o estudo da hipótese de não arbitragem possui contrapartida científica, tanto do lado teórico quanto do empírico. Utilizando-se do modelo estocástico Variância Gama para os preços dos ativos, o teste Bayesiano FBST é implementado com o intuito de se verificar a existência da arbitragem nos mercados, potencialmente expressa nos parâmetros destas densidades. Especificamente, a distribuição do Índice Bovespa é investigada, com os parâmetros risco-neutros sendo estimados baseandose nas opções negociadas no Segmento de Ações e no Segmento de Derivativos da BM&FBovespa. Os resultados aparentam indicar diferenças estatísticas significantes em alguns períodos de tempo. Até que ponto esta evidência é a expressão de uma arbitragem perene nesses mercados ainda é uma questão em aberto. / Precise hypotheses are natural characteristics of the economic theories for determining the value or prices of financial assets. Within these theories the precision is expressed in terms of equilibrium and non-arbitrage hypotheses. The former concept plays an essential role in the theories of finance. Under certain conditions, the Fundamental Theorem of Asset Pricing establishes a coherent and unique asset pricing framework in non-arbitraged markets, grounded on martingales processes. Accordingly, the analysis of the statistical distributions of financial assets can assist in understanding how participants behave in the markets, and may or may not engender conditions to arbitrage. On this regard, the dissertation proposes that the study of non-arbitrage hypothesis has a scientific counterparty, theoretically and empirically. Using a variance gamma stochastic model for prices, the Bayesian test FBST is conducted to verify the presence of arbitrage potentially incorporated on these densities parameters. Specifically, the Bovespa Index distribution is investigated, with risk neutral parameters estimated based on options traded in the Equities Segment and the Derivatives Segment at the BM&FBovespa Exchange. Results seem to indicate significant statistical differences at some periods of time. To what extent this evidence is actually the expression of a perennial arbitrage between the markets still is an open question.

Incapaz de tematizar a conexão interna do valor com as diversas formas sociais que constituem o modo de produção capitalista, a Economia Política não consegue desvendar as tendências imanentes deste modo peculiar de organização da vida material da sociedade, o que a impede de interpretar de maneira consistente o devir histórico da economia capitalista como um todo, bem como o de suas formas particulares consideradas individualmente. Neste trabalho, veremos que tal deficiência fica particularmente clara nas considerações dos economistas sobre o capital acionário (parte I). Marx, ao se propor desenvolver logicamente as formas através das quais a lei do valor pode se impor sobre o metabolismo social, supera a unilateralidade da Economia Política (parte II). No entanto, ele não esclarece exatamente como deve ser pensada a relação entre o desenvolvimento lógico-sistemático das formas da economia burguesa e o devir histórico dessas formas propriamente dito. Por isso, após deduzir a forma-valor capital acionário, proporemos, com base nas semelhanças entre o conceito marxiano de capital e o sujeito absoluto apresentado por Hegel, uma interpretação da história do capital acionário inspirada na filosofia hegeliana da história (parte III). Finalmente, depois de constatar que, apesar de sua proficuidade, a interpretação em moldes hegelianos da história do capital acionário não é plenamente consistente, tentaremos evidenciar a incompatibilidade entre o Espírito Absoluto hegeliano e o conceito marxiano de capital, o que nos permitirá empreender uma interpretação das transformações recentes do capital acionário inspirada na Crítica da Economia Política (parte IV). / Incapable of conceiving the unity of the value-form with the other forms of the capitalist mode of production, Political Economy cannot reveal the internal tendencies of the capitalist economy as such. Consequently, it cannot understand the historical developments of this kind of economic organization. This incapability gets particularly clear when one examines economic theories on share capital. Through the logical development of the forms of value, Marx overcame such limits of Political Economy. What he did not clarify however was how one should conceive the relation between the logical development of the forms of value and the historical development of capital as such. Based on the similarities between Marx\'s concept of capital and Hegel\'s concept of Absolute Spirit, we will test the hypothesis that the latest transformations of share capital can be understood as a result of its increasing conformation to its concept. We shall see that although it can help us understanding some features of these transformations, a hegelian interpretation of it is not fully consistent. That is why, after revealing the most important differences between the hegelian concept of absolute spirit and the marxian concept of capital, we shall try to comprehend how exactly the Critique of Political Economy can help us understanding historical changes in the capitalist mode of production, and particularly the latest historical developments of share capital.

Global warming is affecting the Earth climate year by year, the biggest difference being observable in increasing temperatures in the World Ocean. Following the long- term global ocean warming trend, average sea surface temperatures across the global tropics and subtropics have increased by 0.4–1◦C in the last 40 years. These rates become even higher in semi-enclosed southern seas, such as the Red Sea, threaten- ing the survival of thermal-sensitive species. As average sea surface temperatures are projected to continue to rise, careful study of future developments of extreme temper- atures is paramount for the sustainability of marine ecosystem and biodiversity. In this thesis, we use Extreme-Value Theory to study sea surface temperature extremes from a gridded dataset comprising 16703 locations over the Red Sea. The data were provided by Operational SST and Sea Ice Analysis (OSTIA), a satellite-based data system designed for numerical weather prediction. After pre-processing the data to account for seasonality and global trends, we analyze the marginal distribution of ex- tremes, defined as observations exceeding a high spatially varying threshold, using the Generalized Pareto distribution. This model allows us to extrapolate beyond the ob- served data to compute the 100-year return levels over the entire Red Sea, confirming the increasing trend of extreme temperatures. To understand the dynamics govern- ing the dependence of extreme temperatures in the Red Sea, we propose a flexible local approach based on R-Pareto processes, which extend the univariate Generalized Pareto distribution to the spatial setting. Assuming that the sea surface temperature varies smoothly over space, we perform inference based on the gradient score method over small regional neighborhoods, in which the data are assumed to be stationary in space. This approach allows us to capture spatial non-stationarity, and to reduce the overall computational cost by taking advantage of distributed computing resources. Our results reveal an interesting extremal spatial dependence structure: in particular, from our estimated model, we conclude that significant extremal dependence prevails for distances up to about 2500 km, which roughly corresponds to the Red Sea length.

Hipóteses precisas são características naturais das teorias econômicas de determinação do valor ou preço de ativos financeiros. Nessas teorias, a precisão das hipóteses assume a forma do conceito de equilíbrio ou da não arbitragem. Esse último possui um papel fundamental nas teorias de finanças. Sob certas condições, o Teorema Fundamental do Apreçamento de Ativos estabelece um sistema único e coerente para valorização dos ativos em mercados não arbitrados, valendo-se para tal das formulações para processos de martingal. A análise da distribuição estatística desses ativos financeiros ajuda no entendimento de como os participantes se comportam nos mercados, gerando assim as condições para se arbitrar. Nesse sentido, a tese defendida é a de que o estudo da hipótese de não arbitragem possui contrapartida científica, tanto do lado teórico quanto do empírico. Utilizando-se do modelo estocástico Variância Gama para os preços dos ativos, o teste Bayesiano FBST é implementado com o intuito de se verificar a existência da arbitragem nos mercados, potencialmente expressa nos parâmetros destas densidades. Especificamente, a distribuição do Índice Bovespa é investigada, com os parâmetros risco-neutros sendo estimados baseandose nas opções negociadas no Segmento de Ações e no Segmento de Derivativos da BM&FBovespa. Os resultados aparentam indicar diferenças estatísticas significantes em alguns períodos de tempo. Até que ponto esta evidência é a expressão de uma arbitragem perene nesses mercados ainda é uma questão em aberto. / Precise hypotheses are natural characteristics of the economic theories for determining the value or prices of financial assets. Within these theories the precision is expressed in terms of equilibrium and non-arbitrage hypotheses. The former concept plays an essential role in the theories of finance. Under certain conditions, the Fundamental Theorem of Asset Pricing establishes a coherent and unique asset pricing framework in non-arbitraged markets, grounded on martingales processes. Accordingly, the analysis of the statistical distributions of financial assets can assist in understanding how participants behave in the markets, and may or may not engender conditions to arbitrage. On this regard, the dissertation proposes that the study of non-arbitrage hypothesis has a scientific counterparty, theoretically and empirically. Using a variance gamma stochastic model for prices, the Bayesian test FBST is conducted to verify the presence of arbitrage potentially incorporated on these densities parameters. Specifically, the Bovespa Index distribution is investigated, with risk neutral parameters estimated based on options traded in the Equities Segment and the Derivatives Segment at the BM&FBovespa Exchange. Results seem to indicate significant statistical differences at some periods of time. To what extent this evidence is actually the expression of a perennial arbitrage between the markets still is an open question.

Incapaz de tematizar a conexão interna do valor com as diversas formas sociais que constituem o modo de produção capitalista, a Economia Política não consegue desvendar as tendências imanentes deste modo peculiar de organização da vida material da sociedade, o que a impede de interpretar de maneira consistente o devir histórico da economia capitalista como um todo, bem como o de suas formas particulares consideradas individualmente. Neste trabalho, veremos que tal deficiência fica particularmente clara nas considerações dos economistas sobre o capital acionário (parte I). Marx, ao se propor desenvolver logicamente as formas através das quais a lei do valor pode se impor sobre o metabolismo social, supera a unilateralidade da Economia Política (parte II). No entanto, ele não esclarece exatamente como deve ser pensada a relação entre o desenvolvimento lógico-sistemático das formas da economia burguesa e o devir histórico dessas formas propriamente dito. Por isso, após deduzir a forma-valor capital acionário, proporemos, com base nas semelhanças entre o conceito marxiano de capital e o sujeito absoluto apresentado por Hegel, uma interpretação da história do capital acionário inspirada na filosofia hegeliana da história (parte III). Finalmente, depois de constatar que, apesar de sua proficuidade, a interpretação em moldes hegelianos da história do capital acionário não é plenamente consistente, tentaremos evidenciar a incompatibilidade entre o Espírito Absoluto hegeliano e o conceito marxiano de capital, o que nos permitirá empreender uma interpretação das transformações recentes do capital acionário inspirada na Crítica da Economia Política (parte IV). / Incapable of conceiving the unity of the value-form with the other forms of the capitalist mode of production, Political Economy cannot reveal the internal tendencies of the capitalist economy as such. Consequently, it cannot understand the historical developments of this kind of economic organization. This incapability gets particularly clear when one examines economic theories on share capital. Through the logical development of the forms of value, Marx overcame such limits of Political Economy. What he did not clarify however was how one should conceive the relation between the logical development of the forms of value and the historical development of capital as such. Based on the similarities between Marx\'s concept of capital and Hegel\'s concept of Absolute Spirit, we will test the hypothesis that the latest transformations of share capital can be understood as a result of its increasing conformation to its concept. We shall see that although it can help us understanding some features of these transformations, a hegelian interpretation of it is not fully consistent. That is why, after revealing the most important differences between the hegelian concept of absolute spirit and the marxian concept of capital, we shall try to comprehend how exactly the Critique of Political Economy can help us understanding historical changes in the capitalist mode of production, and particularly the latest historical developments of share capital.