In this study, general geometric Levy market models are considered. Since these models are, in general, incomplete, that is, all contingent claims cannot be replicated by a self-financing portfolio consisting of investments in a risk-free bond and in the stock, it is suggested that the market should be enlarged by artificial assets based on the power-jump processes of the underlying Levy process. Then it is shown that the enlarged market is complete and the explicit hedging portfolios for claims whose payoff function depends on the prices of the stock and the artificial assets at maturity are derived. Furthermore, the portfolio optimization problem is considered in the enlarged market. The problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. It is shown that for particular choices of the equivalent martingale measure in the market, the optimal portfolio only consists of bonds and stocks. This corresponds to completing the market with additional assets in such a way that they are superfluous in the sense that the terminal expected utility is not improved by including these assets in the portfolio.

A Constant Proportion Debt Obligation is a credit derivative which has been introduced to generate a surplus return over a riskless market return. The surplus payments should be obtained by synthetically investing in a risky asset (such as a credit index) and using a linear leverage strategy which is capped for bounding the risk. In this thesis, we investigate two approaches for investigation of constant proportion debt obligations. First, we search for an optimal leverage strategy which minimises the mean-square distance between the final payment and the final wealth of constant proportion debt obligation by the use of optimal control methods. We show that the optimal leverage function for constant proportion debt obligations in a mean-square sense coincides with the one used in practice for geometric type diffusion processes. However, the optimal strategy will lead to a shortfall for some cases. The second approach of this thesis is to develop a pricing formula for constant proportion debt obligations. To do so, we consider both the early defaults and the default on the final payoff features of constant proportion debt obligations. We observe that a constant proportion debt obligation can be modelled as a barrier option with rebate. In this respect, given the knowledge on barrier options, the pricing equation is derived for a particular leverage strategy.

Day-ahead spot electricity markets are the most transparent spot markets where one can find integrated supply and demand curves of the market players for each settlement period. Since it is an indicator for the market players and regulators, in this thesis we model the spot electricity prices. Logarithmic daily average spot electricity prices are modeled as a summation of a deterministic function and multi-factor stochastic process. Randomness in the spot prices is assumed to be governed by three jump processes and a Brownian motion where two of the jump processes are mean reverting. While the Brownian motion captures daily regular price movements, the pure jump process models price shocks which have long term effects and two Ornstein Uhlenbeck type jump processes with different mean reversion speeds capturing the price shocks that affect the price level for relatively shorter time periods. After removing the seasonality which is modeled as a deterministic function from price observations, an iterative threshold function is used to filter the jumps. The threshold function is constructed on volatility estimation generated by a GARCH(1,1) model. Not only the jumps but also the mean reverting returns following the jumps are filtered. Both of the filtered jump processes and residual Brownian components are estimated separately. The model is applied to Austrian, Italian, Spanish and Turkish electricity markets data and it is found that the weekly forecasts, which are generated by the estimated parameters, turn out to be able to capture the characteristics of the observations. After examining the future contracts written on electricity, we also suggest a decision technique which is built on risk premium theory. With the help of this methodology derivative market players can decide on taking whether a long or a short position for a given contract. After testing our technique, we conclude that the decision rule is promising but needs more empirical research.

We consider reduced Hsieh-Clough-Tocher basis functions with respect to a splitting into subtriangles at the barycenter of the original triangular element. This article gives a proof that the second derivatives of those functions, which in general may jump at the subtriangle boundaries, do not jump at the barycenter.

We consider reduced Hsieh-Clough-Tocher basis functions with respect to a splitting into subtriangles at an arbitrary interior point of the original triangular element. This article gives a proof that the second derivatives of those functions, which in general may jump at the subtriangle boundaries, do not jump at the splitting point.

Traditionally, time series of wholesale electricity market spot prices have been modelled either by mimicking market operation and equilibrating demand and supply, or by specifying an exogenous process for prices. More recently, a number of hybrid models have been developed, combining the merits of both methods. In this vein, we present an econometric model for daily spot prices in the New Zealand Electricity Market (NZEM) that utilises reservoir management theory to incorporate information on the hydro storage level, a recognised driver of NZEM spot price behaviour. In order to forecast future storage levels and prices, we also construct a model for daily reservoir releases that can be used in conjunction with time series of inflows. This analysis reveals that releases in New Zealand are driven primarily by hydrological factors, as opposed to market conditions. The combined price and storage forecasting model can be applied in a variety of contexts, and offers an alternative perspective to the traditional models of NZEM behaviour. Finally, we calibrate a Cournot model of market behaviour in the National Electricity Market of Australia during daily peak, shoulder and off-peak periods, adding credibility to the future application of such models. The resulting model parameters are, in general, consistent with conventional wisdom. Spot prices from this market are then modelled by combining the output of the analytical model with a stochastic price process.

We characterize the structure of the domain of a pure jump-type Dirichlet form which is given by a Beurling–Deny formula. In particular, we obtain su cient conditions in terms of the jumping kernel guaranteeing that the test functions are a core for the Dirichlet form and that the form is a Silverstein extension. As an application we show that for recurrent Dirichlet forms the extended Dirichlet space can be interpreted in a natural way as a homogeneous Dirichlet space. For reflected Dirichlet spaces this leads to a simple purely analytic proof that the active reflected Dirichlet space (in the sense of Chen, Fukushima and Kuwae) coincides with the extended active reflected Dirichlet space. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

O objetivo deste estudo foi investigar a organização espaço-temporal dos segmentos da perna e da coxa no saltar à horizontal, verificando as infiuências do organismo e do ambiente (dois tipos de piso: concreto e areia). Participaram do estudo 21 sujeitos, 3 de cada faixa etária: 4, 5, 7, 9, 11, 13 e adulta (X = 19 anos de idade). Os sujeitos foram filmados realizando o saltar à horizontal com marcas desenhadas no centro das articulações do tornozelo, joelho e quadril. Estes pontos foram digitalizados e processados obtendo a posição e velocidade angular dos segmentos da perna e da coxa. A partir da posição e velocidade angular foi possível delinear os gráficos dos atratores (retratos de fase) e calcular os valores dos ângulos de fase para cada segmento, durante a realização da tarefa. Duas reversões para cada segmento, na posição angular, foram identificadas e nestes momentos os valores dos ângulos de fase foram capturados. Analisando as trajetórias dos retratos de fase verificou-se que os segmentos da perna e da coxa apresentaram um conjunto específico de características topológicas, na realização do saltar à horizontal. A análise dos valores dos ângulos de fase, nas duas reversões, indicou que ao longo das faixas etárias e nos dois tipos de piso os segmentos da perna e da coxa apresentaram organização espaço-temporal semelhante, indicando coordenação invariante. / The aim of this investigation was to identify the space-temporal organization of the thigh and shank segments in the standlng long jump, and to verify the organlsmic and environmental (two kinds of pavement: concrete and sand) inlluences on performance. Twenty one subjects, three of each age 4, 5, 7, 9, 11, 13 and adults (X = 19 years old), were recorded performing the standlng long jump with marks on the joint centers of the ankle, knee and hip. Tliese points were digitalized and processed Io obtain angular position and velocity of the shank and of the thigh. From angular position and velocity were delineated and phase angle values were calciilalcd for cach scgment during task performance Two reversals for each segment, in the position angular, were identified and phase angle values were captured. The analysis of phase portrait trajectories showed that shank and thigh have a specific topological set. Based on the analysis of angle phase values, in two reversal monients, it was verified that, across ages and in two kinds of surfaces, shank and thigh segments have the same space-temporal organization, showing invariant coordination. / El objetivo de este estúdio fue investigar Ia organización espacio temporal de los segmentos de Ia perna y de Ia coxa al saltar horizontalmente verificando Ias influencias dei organismo y dei ambiente (dos tipos de piso; cemento y arena). Paticiparon dei estúdio 21 sujetos, 3 de cada clase de edad: 4, 5, 7, 9, 11, 13 y adulta (X = 19 anos de edad). Los sujetos fueron filmados realizando el salto horizontal con marcas dibujadas en el centro de Ias articulaciones dei tobillo, rodilla e anca. Estos puntos fueron digitalizados y procesados obteniendo Ia posición y velocidad angular de los segmentos de Ia pierna y de Ia coxa. A partir de Ia posición y velocidad angular fue posible delinear los gráficos de ios atratores (retratos de fase) y calcular los valores de los ângulos de fase para cada segmento, durante Ia realización de Ia tarefa. Dos reverciones para cada segmento, en Ia posición angular, fueron identificadas y en estos momentos los valores de los ângulos de fase fueron registrados. Analisando Ias trayectorias de los retratos de fase se verifico que los segmentos de Ia pierna y de Ia coxa presentaron un conjunto específico de características topologicas, en Ia ejecución dei salto horizontal. El análisis de los valores de los ângulos de fase, en Ias dos reversiones, indico que a Io largo de ias classes de edad y en los dos tipos de piso los segmentos de Ia pierna y de Ia coxa presentaron organización espacio-temporal semejante, indicando coordinación invariante.

O objetivo deste estudo foi investigar a organização espaço-temporal dos segmentos da perna e da coxa no saltar à horizontal, verificando as infiuências do organismo e do ambiente (dois tipos de piso: concreto e areia). Participaram do estudo 21 sujeitos, 3 de cada faixa etária: 4, 5, 7, 9, 11, 13 e adulta (X = 19 anos de idade). Os sujeitos foram filmados realizando o saltar à horizontal com marcas desenhadas no centro das articulações do tornozelo, joelho e quadril. Estes pontos foram digitalizados e processados obtendo a posição e velocidade angular dos segmentos da perna e da coxa. A partir da posição e velocidade angular foi possível delinear os gráficos dos atratores (retratos de fase) e calcular os valores dos ângulos de fase para cada segmento, durante a realização da tarefa. Duas reversões para cada segmento, na posição angular, foram identificadas e nestes momentos os valores dos ângulos de fase foram capturados. Analisando as trajetórias dos retratos de fase verificou-se que os segmentos da perna e da coxa apresentaram um conjunto específico de características topológicas, na realização do saltar à horizontal. A análise dos valores dos ângulos de fase, nas duas reversões, indicou que ao longo das faixas etárias e nos dois tipos de piso os segmentos da perna e da coxa apresentaram organização espaço-temporal semelhante, indicando coordenação invariante. / The aim of this investigation was to identify the space-temporal organization of the thigh and shank segments in the standlng long jump, and to verify the organlsmic and environmental (two kinds of pavement: concrete and sand) inlluences on performance. Twenty one subjects, three of each age 4, 5, 7, 9, 11, 13 and adults (X = 19 years old), were recorded performing the standlng long jump with marks on the joint centers of the ankle, knee and hip. Tliese points were digitalized and processed Io obtain angular position and velocity of the shank and of the thigh. From angular position and velocity were delineated and phase angle values were calciilalcd for cach scgment during task performance Two reversals for each segment, in the position angular, were identified and phase angle values were captured. The analysis of phase portrait trajectories showed that shank and thigh have a specific topological set. Based on the analysis of angle phase values, in two reversal monients, it was verified that, across ages and in two kinds of surfaces, shank and thigh segments have the same space-temporal organization, showing invariant coordination. / El objetivo de este estúdio fue investigar Ia organización espacio temporal de los segmentos de Ia perna y de Ia coxa al saltar horizontalmente verificando Ias influencias dei organismo y dei ambiente (dos tipos de piso; cemento y arena). Paticiparon dei estúdio 21 sujetos, 3 de cada clase de edad: 4, 5, 7, 9, 11, 13 y adulta (X = 19 anos de edad). Los sujetos fueron filmados realizando el salto horizontal con marcas dibujadas en el centro de Ias articulaciones dei tobillo, rodilla e anca. Estos puntos fueron digitalizados y procesados obteniendo Ia posición y velocidad angular de los segmentos de Ia pierna y de Ia coxa. A partir de Ia posición y velocidad angular fue posible delinear los gráficos de ios atratores (retratos de fase) y calcular los valores de los ângulos de fase para cada segmento, durante Ia realización de Ia tarefa. Dos reverciones para cada segmento, en Ia posición angular, fueron identificadas y en estos momentos los valores de los ângulos de fase fueron registrados. Analisando Ias trayectorias de los retratos de fase se verifico que los segmentos de Ia pierna y de Ia coxa presentaron un conjunto específico de características topologicas, en Ia ejecución dei salto horizontal. El análisis de los valores de los ângulos de fase, en Ias dos reversiones, indico que a Io largo de ias classes de edad y en los dos tipos de piso los segmentos de Ia pierna y de Ia coxa presentaron organización espacio-temporal semejante, indicando coordinación invariante.

Made available in DSpace on 2016-12-06T17:07:16Z (GMT). No. of bitstreams: 1 Roberta Castilhos.pdf: 2584152 bytes, checksum: cac31b324bf86034d356041746b8ff53 (MD5) Previous issue date: 2008-03-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The aim of this descriptive exploratory study was to evaluate kinematic characteristics of the long jump of children in different motor development stages according to the Gallahue s analytical matrix. Specifically it aimed to verify the motor development stage of children regarding body segment and the different phases of the long jump; to identify and compare the inter-segmental angles of the long jump; to verify the contribution of angle parameters to the long jump performance in the different motor development stages. The sample was composed of 90 male and female children ranging in age from 5 to 13 years old (average age of 8,52±2,36 years old), whose parents consented to their participation in the study through the presentation of the correct fulfilling and signature of the assent term. The study was submitted and approved by the UDESC s Research Ethics Committee. For data collection a video camera and Gallahue s analytical matrix for the long jump, which allows classifying children in three maturation stages (initial, elementary and mature) were used as instruments. The knee, trunk, hip and upper limb angle in the propulsive, flight and landing phases and the reached distance were the selected variables. After receiving authorization from the parents and school, the children were conducted to the UDESC s Biomechanics Laboratory, where they had a time to get used to the environment and the equipments. After the fulfilling of children`s identification form and anatomical markers set up the acquisition of anthropometric and kinematic data to a sampling frequency of 60 Hz were carried out. Before the acquisition the task was demonstrated through a video and then the children performed 3 valid horizontal jumps. Data were filtered by a fourth-order low-pass Butterworth filter with a cut-off frequency varying between 6 and 10 Hz. Data analysis was composed of two parts: (1) a qualitative evaluation through the corporal segment`s classification; and (2) a quantitative analysis of the variables through the caption of angle parameters. For both analysis it was considered the specifically instants of the propulsive, flight and landing phases of the jump, according to Estrázulas (2006) procedure. Data were characterized and analyzed through descriptive statistics (frequency distribution, mean, standard deviation, coefficient of variation, minimum and maximum, superior and inferior limits of the 95% confidence interval for mean and box-plot graphics). To compare the mean among the three stages ANOVA One Way followed by Scheffé s post hoc tests were used. To verify the contribution of the different angle parameters the Multiple Linear Regression was used. The confidence level of 95% was adopted for all the tests. Statistically significant differences were found when comparing the segmental angles between all the stages in the three jump phases. In synthesis the corporal segments showed different maturation time and the lower limb were the most delayed ones. The knee, trunk, hip and upper limb angles showed to be good indicators of the motor development stages. Only the upper limb angle in the flight phase significantly contributed to the jump performance and it could be explained by the major importance of the arm movement in the horizontal jump execution. / O objetivo deste estudo descritivo exploratório foi avaliar as características cinemáticas do salto horizontal de crianças em diferentes estágios de desenvolvimento motor. Especificamente: verificar o estágio de desenvolvimento motor das crianças por segmento corporal e nas diferentes fases do salto horizontal; identificar e comparar os ângulos inter segmentares do salto horizontal de crianças entre diferentes estágios; verificar a contribuição dos parâmetros angulares no desempenho do salto horizontal nos diferentes estágios. Participaram 90 crianças da Grande Florianópolis-SC, ambos os sexos, idade entre 5 e 13 anos (8,52±2,36 anos), cujos pais consentiram a participação na pesquisa, mediante apresentação da autorização e termo de consentimento preenchidos e assinados. O estudo foi aprovado pelo Comitê de Ética em Pesquisa da UDESC. Utilizou-se como instrumentos uma câmera de vídeo e a matriz de análise qualitativa do salto horizontal de Gallahue. Selecionouse as variáveis: ângulo de joelho, ângulo de quadril, ângulo de tronco e ângulo de membro superiores nas fases de propulsão, de vôo e de aterrissagem do salto horizontal e distância alcançada. Após devidamente autorizadas as crianças foram encaminhadas ao Laboratório de Biomecânica da UDESC. As crianças passaram por um período de familiarização com o ambiente e equipamentos. Após o preenchimento da ficha de identificação e a demarcação dos pontos anatômicos foi realizada a aquisição dos dados antropométricos e cinemáticos, esses a uma freqüência de 60 Hz. Previamente à coleta fez-se a demonstração da tarefa através de um vídeo e em seguida as crianças executaram 3 saltos horizontais válidos. Os dados cinemáticos foram filtrados com Butterworth 4ª ordem, passa baixa com freqüência de corte variando entre 6 e 10 Hz. A análise dos dados constituiu-se de uma parte qualitativa e uma quantitativa: a primeira composta pela classificação dos segmentos corporais em estágios inicial, elementar e maduro; a segunda, a captura dos ângulos, ambas em instantes específicos das fases de propulsão, vôo e aterrissagem do salto, conforme sistemática de Estrázulas (2006), baseada na matriz analítica de Gallahue. Utilizou-se a estatística descritiva: distribuição de freqüências, média, desvio padrão, coeficiente de variação, mínimo e máximo, limites inferior e superior do intervalo de 95% de confiança para a média e gráficos Box-plot. Para comparação entre as médias dos três estágios aplicou-se a ANOVA One way e para verificar entre quais estágios estas diferenças se encontravam, o post hoc de Scheffé; para verificar a contribuição dos parâmetros angulares na performance do salto, a Regressão Linear Múltipla - Stepwise. Adotou-se p 0,05. Na comparação dos ângulos segmentares encontraram-se diferenças estatisticamente significativas entre todos os estágios em todas as fases do salto. Conclui-se que os segmentos corporais apresentaram diferentes tempos de maturação, tendo os membros inferiores maturação mais tardia. Os ângulos de joelho, quadril, tronco e membros superiores mostraram-se bons indicadores do estágio de desenvolvimento motor. Apenas o ângulo de membro superior na fase de vôo apresentou contribuição significativa para o desempenho do salto, que pode ser decorrente da grande importância da utilização dos braços na execução do salto horizontal.