Tendo em vista o crescente investimento em atividades economicamente importantes nas zonas costeiras, tal como a produção petrolífera brasileira e o crescimento na atividade portuária e esforço de pesca, a compreensão adequada dos fenômenos oceanográficos e meteorológicos sobre tais zonas é de grande valia para as operações desses setores. Os ventos representam um importante parâmetro para análise nesse sentido, sendo a principal fonte de energia para a geração de ondas de gravidade nos oceanos, e determinantes na caracterização de condições severas tempo. Uma série de estudos foram desenvolvidos nos últimos anos envolvendo a análise do comportamento dos extremos de ondas sobre a região do Oceano Atlântico Sul, de acordo com o crescimento da demanda por tais informações pelo setor industrial. No entanto, há poucos registros de estudos que caracterizem os extremos de intensidade de vento sobre essa região. E, em nenhum desses trabalhos, a separação direcional do vento extremo e seus fenômenos causadores foram levados em consideração. Dessa forma, o presente trabalho visa atender diretamente a necessidade por trabalhos nesse sentido para a região do Oceano Atlântico Sul, buscando oferecer uma análise dos campos de ventos extremos direcionalmente segregados, através de dados do projeto de reanálise \\textit{NCEP/NCAR Reanalysis I} e de resultados de uma simulação numérica com o modelo BRAMS. A tais conjuntos de dados foi aplicada a metodologia de análise de extremos \\textit{Peaks Over Threshold} (POT), que trata do ajuste dos excessos acima de um limiar estabelecido a uma distribuição conhecida, a Distribuição Generalizada de Pareto (Generalized Pareto Distribution - GPD). E, a partir disso, construir mapas com os valores extremos de retorno para longos períodos. Tais parâmetros são muito importantes na predição de eventos extremos e no refinamento de simulações de longo período. Os extremos relacionados aos fenômenos em larga escala, dados pelos campos do NCEP, em conjunto com o maior detalhamento em mesoescala, dado pelo BRAMS, refletiram diretamente no comportamento dos valores extremos de retorno. Para todas as direções do vento analisadas, observaram-se feições mais refinadas dos extremos de retorno para os resultados com a simulação do BRAMS, principalmente nas zonas costeiras. Essas feições, principalmente àquelas ao sul e sudeste do Oceano Atlântico Sul, tiveram seus valores potencializados em zonas já conhecidas na bibliografia pela grande incidência de eventos altamente energéticos. / Given the growing investment in important economic activities in coastal areas, such as oil and gas exploitation, harbor activities and increasing fishing effort, the proper understanding of oceanographic and meteorological phenomena over such areas has great value to the operations of such sectors. The winds are an important parameter for analysis in this context, being the main source of energy for gravity waves generation in the ocean, and determining the characterization of severe weather conditions. A number of studies have been developed in recent years involving the behavior of extreme waves over the South Atlantic Ocean region, given the rowing demand for such information by industrial sectors. However, there are few records of studies that characterize the extremes of wind speed fields over this region. And, in none of these works, the direction of the extreme wind and meteorological phenomenon associated were considered. Thus, this paper aims to address directly the need for work in this context for the South Atlantic Ocean region, seeking to offer an analysis of extreme wind fields directionally separated, through data from the NCEP/NCAR Reanalysis 1 and results from a numerical simulation with BRAMS. The Peaks Over Threshold (POT), which deals with the adjustment of the excesses above a threshold to the Generalized Pareto Distribution (GPD), was applied to both datasets. And from that, maps with the extreme return values have been developed for long return periods. These parameters are very important in predicting extreme events and refinement of long-period simulations. Extreme winds related to the large scale phenomena, represented by NCEP fields, in conjunction with the greater mesoscale detail, given by the BRAMS simulation, directly reflected in the behavior of extreme return values. For all wind directions analyzed, there were more refined features of the extremes return levels given by the BRAMS simulation, especially in coastal areas. These features, notably those in the south and southeast of the South Atlantic Ocean, values were strengthened in areas already known in the literature for the high incidence of energetic events.

Tendo em vista o crescente investimento em atividades economicamente importantes nas zonas costeiras, tal como a produção petrolífera brasileira e o crescimento na atividade portuária e esforço de pesca, a compreensão adequada dos fenômenos oceanográficos e meteorológicos sobre tais zonas é de grande valia para as operações desses setores. Os ventos representam um importante parâmetro para análise nesse sentido, sendo a principal fonte de energia para a geração de ondas de gravidade nos oceanos, e determinantes na caracterização de condições severas tempo. Uma série de estudos foram desenvolvidos nos últimos anos envolvendo a análise do comportamento dos extremos de ondas sobre a região do Oceano Atlântico Sul, de acordo com o crescimento da demanda por tais informações pelo setor industrial. No entanto, há poucos registros de estudos que caracterizem os extremos de intensidade de vento sobre essa região. E, em nenhum desses trabalhos, a separação direcional do vento extremo e seus fenômenos causadores foram levados em consideração. Dessa forma, o presente trabalho visa atender diretamente a necessidade por trabalhos nesse sentido para a região do Oceano Atlântico Sul, buscando oferecer uma análise dos campos de ventos extremos direcionalmente segregados, através de dados do projeto de reanálise \\textit{NCEP/NCAR Reanalysis I} e de resultados de uma simulação numérica com o modelo BRAMS. A tais conjuntos de dados foi aplicada a metodologia de análise de extremos \\textit{Peaks Over Threshold} (POT), que trata do ajuste dos excessos acima de um limiar estabelecido a uma distribuição conhecida, a Distribuição Generalizada de Pareto (Generalized Pareto Distribution - GPD). E, a partir disso, construir mapas com os valores extremos de retorno para longos períodos. Tais parâmetros são muito importantes na predição de eventos extremos e no refinamento de simulações de longo período. Os extremos relacionados aos fenômenos em larga escala, dados pelos campos do NCEP, em conjunto com o maior detalhamento em mesoescala, dado pelo BRAMS, refletiram diretamente no comportamento dos valores extremos de retorno. Para todas as direções do vento analisadas, observaram-se feições mais refinadas dos extremos de retorno para os resultados com a simulação do BRAMS, principalmente nas zonas costeiras. Essas feições, principalmente àquelas ao sul e sudeste do Oceano Atlântico Sul, tiveram seus valores potencializados em zonas já conhecidas na bibliografia pela grande incidência de eventos altamente energéticos. / Given the growing investment in important economic activities in coastal areas, such as oil and gas exploitation, harbor activities and increasing fishing effort, the proper understanding of oceanographic and meteorological phenomena over such areas has great value to the operations of such sectors. The winds are an important parameter for analysis in this context, being the main source of energy for gravity waves generation in the ocean, and determining the characterization of severe weather conditions. A number of studies have been developed in recent years involving the behavior of extreme waves over the South Atlantic Ocean region, given the rowing demand for such information by industrial sectors. However, there are few records of studies that characterize the extremes of wind speed fields over this region. And, in none of these works, the direction of the extreme wind and meteorological phenomenon associated were considered. Thus, this paper aims to address directly the need for work in this context for the South Atlantic Ocean region, seeking to offer an analysis of extreme wind fields directionally separated, through data from the NCEP/NCAR Reanalysis 1 and results from a numerical simulation with BRAMS. The Peaks Over Threshold (POT), which deals with the adjustment of the excesses above a threshold to the Generalized Pareto Distribution (GPD), was applied to both datasets. And from that, maps with the extreme return values have been developed for long return periods. These parameters are very important in predicting extreme events and refinement of long-period simulations. Extreme winds related to the large scale phenomena, represented by NCEP fields, in conjunction with the greater mesoscale detail, given by the BRAMS simulation, directly reflected in the behavior of extreme return values. For all wind directions analyzed, there were more refined features of the extremes return levels given by the BRAMS simulation, especially in coastal areas. These features, notably those in the south and southeast of the South Atlantic Ocean, values were strengthened in areas already known in the literature for the high incidence of energetic events.

One of today’s financial trends is securitization. Evaluating Securitization risk requires some strong quantitative skills and a deep understanding of both credit and market risk. For international securitization programs it is mandatory to take into account the exchange-rates-related risks. We will see the di˙erent methods to evaluate extreme variations of the exchange rates using the Extreme Value Theory and Monte Carlo simulations. / Värdepapperisering är en av dagens finansiella trender. Att utvärdera vär-depapperisering risk kräver starka kvantitativa kunskaper och en förståelseför både kredit- och marknadsrisk. För internationell värdepapperisering ärdet obligatoriskt att hänsyn tas till valutarisker. Vi kommer att se de olika metoder för att utvärdera extrema variationer i valutakurser med hjälp av extremvärdesteori och Monte Carlo-simuleringar.

The peaks over threshold (POT) method provides an attractive framework for estimating the risk of extreme events such as severe storms or large insurance claims. However, the conventional POT procedure, where the threshold excesses are modelled by a generalized Pareto distribution, suffers from small samples and subjective threshold selection. In recent years, two alternative approaches have been proposed in the form of mixture models that estimate the threshold and a folding procedure that generates larger tail samples. In this paper the empirical performances of the conventional POT procedure, the folding procedure and a mixture model are compared by modelling data sets on fire insurance claims and hurricane damage costs. The results show that the folding procedure gives smaller standard errors of the parameter estimates and in some cases more stable quantile estimates than the conventional POT procedure. The mixture model estimates are dependent on the starting values in the numerical maximum likelihood estimation, and are therefore difficult to compare with those from the other procedures. The conclusion is that none of the procedures is overall better than the others but that there are situations where one method may be preferred.

The work presented in this thesis studies the load and loadeffects of traffic loads on railway bridges. The increasedknowledge of the traffic loads, simulated using fieldmeasurements of actual trains, are employed in a reliabilityanalysis in an attempt at upgrading existing railwaybridges. The study utilises data from a weigh-in-motion site whichrecords, for each train, the train speed, the loads from eachaxle and the axle spacings. This data of actual trainconfigurations and axle loads are portrayed as moving forcesand then used in computer simulations of trains crossing twodimensional simply supported bridges at constant speed. Onlysingle track short to medium span bridges are considered in thethesis. The studied load effect is the moment at mid-span. Fromthe computer simulations the moment history at mid-span isobtained. The load effects are analysed by two methods, the first isthe classical extreme value theory where the load effect ismodelled by the family of distributions called the generalisedextreme value distribution (GEV). The other method adopts thepeaks-over-threshold method (POT) where the limiting family ofdistributions for the heights to peaks-over-threshold is theGeneralised Pareto Distribution (GPD). The two models aregenerally found to be a good representation of the data. The load effects modelled by either the GEV or the GPD arethen incorporated into a reliability analysis in order to studythe possibility of raising allowable axle loads on existingSwedish railway bridges. The results of the reliabilityanalysis show that they are sensitive to the estimation of theshape parameter of the GEV or the GPD. While the study is limited to the case of the ultimate limitstate where the effects of fatigue are not accounted for, thefindings show that for the studied cases an increase inallowable axle load to 25 tonnes would be acceptable even forbridges built to the standards of 1940 and designed to LoadModel A of that standard. Even an increase to both 27.5 and 30tonnes appears to be possible for certain cases. It is alsoobserved that the short span bridges ofapproximately fourmetres are the most susceptible to a proposed increase inpermissible axle load. <b>Keywords:</b>bridge, rail, traffic load, load effect,dynamic amplification factor, extreme value theory,peaks-over-threshold, reliability theory, axle loads, fielddata.

<p>The work presented in this thesis studies the load and loadeffects of traffic loads on railway bridges. The increasedknowledge of the traffic loads, simulated using fieldmeasurements of actual trains, are employed in a reliabilityanalysis in an attempt at upgrading existing railwaybridges.</p><p>The study utilises data from a weigh-in-motion site whichrecords, for each train, the train speed, the loads from eachaxle and the axle spacings. This data of actual trainconfigurations and axle loads are portrayed as moving forcesand then used in computer simulations of trains crossing twodimensional simply supported bridges at constant speed. Onlysingle track short to medium span bridges are considered in thethesis. The studied load effect is the moment at mid-span. Fromthe computer simulations the moment history at mid-span isobtained.</p><p>The load effects are analysed by two methods, the first isthe classical extreme value theory where the load effect ismodelled by the family of distributions called the generalisedextreme value distribution (GEV). The other method adopts thepeaks-over-threshold method (POT) where the limiting family ofdistributions for the heights to peaks-over-threshold is theGeneralised Pareto Distribution (GPD). The two models aregenerally found to be a good representation of the data.</p><p>The load effects modelled by either the GEV or the GPD arethen incorporated into a reliability analysis in order to studythe possibility of raising allowable axle loads on existingSwedish railway bridges. The results of the reliabilityanalysis show that they are sensitive to the estimation of theshape parameter of the GEV or the GPD.</p><p>While the study is limited to the case of the ultimate limitstate where the effects of fatigue are not accounted for, thefindings show that for the studied cases an increase inallowable axle load to 25 tonnes would be acceptable even forbridges built to the standards of 1940 and designed to LoadModel A of that standard. Even an increase to both 27.5 and 30tonnes appears to be possible for certain cases. It is alsoobserved that the short span bridges ofapproximately fourmetres are the most susceptible to a proposed increase inpermissible axle load.</p><p><b>Keywords:</b>bridge, rail, traffic load, load effect,dynamic amplification factor, extreme value theory,peaks-over-threshold, reliability theory, axle loads, fielddata.</p>

My dissertation is based on a unified self-consistent scaling framework which is consistent with key behavior exhibited by many spatially/temporally varying earth, environmental and other variables. This behavior includes tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that often decay with lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags, with breakdown in power-law scaling at small and/or large lags; linear relationships between log structure functions of successive orders at all lags, also known as extended self-similarity; and nonlinear scaling of structure function power-law exponents with function order. The major question we attempt to answer is: given data measured on a given support scale at various points throughout a 1D/2D/3D sampling domain, which appear to be statistically distributed and to scale in a manner consistent with that scaling framework, what can be said about the spatial statistics and scaling of its extreme values, on arbitrary separation or domain scales? To do so, we limit our investigation in 1D domain for simplicity and generate synthetic signals as samples from 1D sub-Gaussian random fields subordinated to truncated monofractal fractional Brownian motion (tfBm) or truncated fractional Gaussian noise (tfGn). Such sub-Gaussian fields are scale mixtures of stationary Gaussian fields with random variances that we model as being log-normal or Lévy α/2-stable. This novel interpretation of the data allows us to obtain maximum likelihood estimates of all parameters characterizing the underlying truncated sub-Gaussian fields. Based on synthetic data, we find these samples conform to the aforementioned scaling framework and confirm the effectiveness of generation schemes. We numerically investigate the manner in which variables, which scale according to the above scaling framework, behave at the tails of their distributions. Ours is the first study to explore the statistical scaling of extreme values, specifically peaks over thresholds or POTs, associated with such families of sub-Gaussian fields. Before closing this work, we apply and verify our analysis by investigating the scaling of statistics characterizing vertical increments in neutron porosity data, and POTs in absolute increments, from six deep boreholes in three different depositional environments.

Value-at-Risk (VaR) has long been the standard risk measure in financial risk management. However, VaR suffers from critical shortcomings as a risk measure when it comes to quantifying the most severe risks, which was made especially apparent during the financial crisis of 2007–2008. An alternative risk measure addressing the shortcomings of VaR known as expected shortfall (ES) is gaining popularity and is set to replace VaR as the standard measure of financial risk. This thesis introduces how extreme value theory can be applied in estimating ES using an unconditional peaks-over-threshold method. This includes giving an introduction to the theoretical foundations of the method. An application of this method is also performed on five different assets. These assets are chosen to serve as a proxy for the more broad asset classes of equity, fixed income, currencies, commodities and cryptocurrencies. In terms of ES, we find that cryptocurrencies is the riskiest asset and fixed income the safest.

This thesis investigates applying the semiparametric method Peaks-Over-Threshold on data generated from a Monte Carlo simulation when estimating the financial risk measures Value-at-Risk and Expected Shortfall. The goal is to achieve a faster convergence than a Monte Carlo simulation when assessing extreme events that symbolise the worst outcomes of a financial portfolio. Achieving a faster convergence will enable a reduction of iterations in the Monte Carlo simulation, thus enabling a more efficient way of estimating risk measures for the portfolio manager.  The financial portfolio consists of US life insurance policies offered on the secondary market, gathered by our partner RessCapital. The method is evaluated on three different portfolios with different defining characteristics.  In Part I an analysis of selecting an optimal threshold is made. The accuracy and precision of Peaks-Over-Threshold is compared to the Monte Carlo simulation with 10,000 iterations, using a simulation of 100,000 iterations as the reference value. Depending on the risk measure and the percentile of interest, different optimal thresholds are selected.  Part II presents the result with the optimal thresholds from Part I. One can conclude that Peaks-Over-Threshold performed significantly better than a Monte Carlo simulation for Value-at-Risk with 10,000 iterations. The results for Expected Shortfall did not achieve a clear improvement in terms of precision, but it did show improvement in terms of accuracy.  Value-at-Risk and Expected Shortfall at the 99.5th percentile achieved a greater error reduction than at the 99th. The result therefore aligned well with theory, as the more "rare" event considered, the better the Peaks-Over-Threshold method performed.  In conclusion, the method of applying Peaks-Over-Threshold can be proven useful when looking to reduce the number of iterations since it do increase the convergence of a Monte Carlo simulation. The result is however dependent on the rarity of the event of interest, and the level of precision/accuracy required. / Det här examensarbetet tillämpar metoden Peaks-Over-Threshold på data genererat från en Monte Carlo simulering för att estimera de finansiella riskmåtten Value-at-Risk och Expected Shortfall. Målet med arbetet är att uppnå en snabbare konvergens jämfört med en Monte Carlo simulering när intresset är s.k. extrema händelser som symboliserar de värsta utfallen för en finansiell portfölj. Uppnås en snabbare konvergens kan antalet iterationer i simuleringen minskas, vilket möjliggör ett mer effektivt sätt att estimera riskmåtten för portföljförvaltaren.  Den finansiella portföljen består av amerikanska livförsäkringskontrakt som har erbjudits på andrahandsmarknaden, insamlat av vår partner RessCapital. Metoden utvärderas på tre olika portföljer med olika karaktär.  I Del I så utförs en analys för att välja en optimal tröskel för Peaks-Over-Threshold. Noggrannheten och precisionen för Peaks-Over-Threshold jämförs med en Monte Carlo simulering med 10,000 iterationer, där en Monte Carlo simulering med 100,000 iterationer används som referensvärde. Beroende på riskmått samt vilken percentil som är av intresse så väljs olika trösklar.  I Del II presenteras resultaten med de "optimalt" valda trösklarna från Del I. Peaks-over-Threshold påvisade signifikant bättre resultat för Value-at-Risk jämfört med Monte Carlo simuleringen med 10,000 iterationer. Resultaten för Expected Shortfall påvisade inte en signifikant förbättring sett till precision, men visade förbättring sett till noggrannhet.  För både Value-at-Risk och Expected Shortfall uppnådde Peaks-Over-Threshold en större felminskning vid 99.5:e percentilen jämfört med den 99:e. Resultaten var därför i linje med de teoretiska förväntningarna då en högre percentil motsvarar ett extremare event.  Sammanfattningsvis så kan metoden Peaks-Over-Threshold vara användbar när det kommer till att minska antalet iterationer i en Monte Carlo simulering då resultatet visade att Peaks-Over-Threshold appliceringen accelererar Monte Carlon simuleringens konvergens. Resultatet är dock starkt beroende av det undersökta eventets sannolikhet, samt precision- och noggrannhetskravet.

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.