Electricity markets around the world have gone through, or are currently in a deregulation phase. As a result, power companies that formerly enjoyed a monopoly are now facing risks. In order to cover (hedge) these risks, futures markets have emerged, in parallel with the spot price markets. Then, markets of more complex derived products have appeared to better hedge the risk exposures of power suppliers and consumers. An Affine Jump Diffusion (AJD) framework is presented here to coherently model the dynamics of the spot price of electricity and all the futures contracts. The non-storability of electricity makes it indeed impossible to use it in hedging strategies. Futures contracts, however, are standard financial contracts that can be stored and used in hedging strategies. We thus propose to consider the set of futures contracts as the primary commodities to be modelled and jointly estimate the parameters of the spot and futures prices based on their historical time series. The estimation is done by Maximum Likelihood, using a Kalman Filter recursive algorithm that has been updated to account for non-Gaussian errors. This procedure has been applied to the German European Energy index (EEX) based in Frankfurt for electricity, to the Brent for Crude oil, and to the NBP for natural gas. The AJD framework is very powerful because the characteristic function of the underlying stochastic variables can be obtained just by solving a system of complex valued ODEs. We took advantage of this feature and developed a novel approach to estimate expectations of arbitrary functions of random variables that does not require the probability density function of the stochastic variables, but instead, their characteristic function. This approach, relying on the Parseval Identity, provided closed form solutions for options with payoff functions that have an analytical Fourier transform. In particular, European calls, puts and spread options could be computed as well as the value of multi-fuel power plants that can be viewed as an option to exchange the most economic fuel of the moment against electricity. A numerical procedure has also been developed for options with payoff functions that do not have an analytical Fourier transform. This numerical approach is indeed using a Fast Fourier Transform of the payoff function, and can be used in Dynamic Programming algorithms to price contracts with endogenous exercise strategies. Finally, it is showed that the (mathematical) partial derivatives of these contracts, often referred to as the Greeks, could also be computed at low cost. This allows to build hedging strategies to shape the risk profile of a given producer, or consumer.

Aunque la transmisión del virus de la lengua azul (VLA) aparentemente se interrumpe durante el invierno, los brotes a menudo reaparecen en la siguiente temporada. Para evaluar la probabilidad de que el VLA sobreviva al invierno a través de la persistencia en vectores adultos, hospedadores o una combinación de ambos, se desarrolló un modelo de evaluación del riesgo estocástico. Además, el modelo permite evaluar el papel que juega el número residual de vectores presentes durante el invierno, y el papel desempeñado por los Culicoides con comportamiento endofílico. El modelo se aplicó a un escenario real, la persistencia del VLA en Alemania entre 2006 y 2007. Los resultados mostraron que la presencia de vectores durante el invierno permitiría la transmisión durante este periodo, y que mientras que la transmisión se vería favorecida por el comportamiento endofílico, su efecto era limitado. A pesar de que la transmisión por los mecanismos estudiados era posible, la probabilidad parecía demasiado baja para explicar la reaparición de la enfermedad observada en Alemania. Las redes de transporte y comercio continúan expandiéndose, y una consecuencia importante es la importación de patógenos transmitidos por vectores. Un aspecto importante de la epidemiología de la lengua azul (LA) es la posibilidad de que Culicoides infectados sean introducidos a través de redes de transporte y comerciales. Por tanto, se desarrolló un modelo estocástico de evaluación de riesgos para calcular la probabilidad de aparición de un brote de lengua azul, por introducción de Culicoides a través de estas redes. El modelo se aplicó al riesgo de una epidemia del serotipo 8 en España en 2007 por el transporte de Culicoides desde los países afectados del norte de Europa, independientemente del mecanismo de introducción del vector. El riesgo anual ponderado parecía ser bajo (entre 3.2x10-7 y 6.4x10-12), aunque había grandes diferencias dependiendo del país de origen, con las probabilidades más elevadas desde Bélgica, Holanda, Alemania y Francia. Para que este mecanismo supusiera un riesgo significativo para los países libres, el número de vectores transportados tendría que ser elevado. La hipótesis de que los toros infectados pueden excretar virus a través de su esperma dio lugar a restricciones en el comercio internacional de semen y al establecimiento de medidas preventivas. Sin embargo, ni el riesgo de transmisión de LA por el semen, ni la eficacia de estas medidas se han evaluado cuantitativamente. El objetivo del estudio fue calcular por medio de un modelo estocástico, en caso de introducción de la LA en un centro de recogida de semen bovino (CRS), tanto el riesgo de transmisión del VLA a través de semen de bovino, como la reducción de dicho riesgo por aplicación de medidas preventivas. El modelo se aplicó a diferentes escenarios, dependiendo por ejemplo del tipo de prueba diagnóstica empleada, el intervalo entre los controles de los toros donantes, o la tasa de dispersión del VLA dentro del CRS. Los controles cada 60 días por ensayo por inmunoabsorción ligado a enzimas (ELISA) parece ser un método poco eficaz para reducir el riesgo de transmisión por semen en comparación con la reacción en cadena de polimerasa (PCR) cada 28 días. Un aumento en la tasa de propagación del VLA dentro del CRS reduce el riesgo de transmisión por el semen. El almacenamiento de semen por 30 días antes de su distribución parece ser eficaz para reducir el riesgo de transmisión. El análisis de sensibilidad identificó la probabilidad de excreción del VLA en semen como un parámetro crucial. Sin embargo, existe un alto grado de incertidumbre asociado a este parámetro, con diferencias significativas en función del serotipo del virus. / Even though bluetongue virus (BTV) transmission is apparently interrupted during winter, bluetongue outbreaks often reappear in the next season (overwintering). In order to assess the probability of BTV overwintering by persistence in adult vectors, ruminants (through prolonged viraemia) or a combination of both, a quantitative risk assessment model was developed. Furthermore, the model allowed the role played by the residual number of vectors present during winter to be examined, and the effect of a proportion of Culicoides living inside buildings (endophilic behaviour) to be explored. The model was then applied to a real scenario: overwintering in Germany between 2006 and 2007. The results showed that the limited number of vectors active during winter seemed to allow the transmission of BTV during this period, and that while transmission was favoured by the endophilic behaviour of some Culicoides, its effect was limited. Even though transmission was possible, the likelihood of BTV overwintering by the mechanisms studied seemed too low to explain the observed re-emergence of the disease. Transport and trade networks continue to expand, and one important consequences of this expansion is vector-borne pathogen importation. One important aspect of BT epidemiology is the potential for movement of infected adults Culicoides via local and global transportation networks. Therefore, a stochastic risk assessment model was constructed to assess the probability of development of a BTV outbreak as a consequence of the introduction of infected Culicoides via transport and trade networks. The model was applied to calculate the risk of a BTV-8 epidemic in Spain in 2007 as the consequence of the transport of a Culicoides from the affected Northern European countries, regardless of the mechanism by which the midge was introduced. The weighted annual risk by transportation of a single Culicoides from the affected Northern European countries seemed to be low (between 3.2x10-7 and 6.4x10-12) although there were major differences among countries, with the highest risks by Culicoides imported from Belgium, the Netherlands, Germany and France. For this mechanism to pose a significant risk to BTV-free countries, large number of vectors would have to be transported. The hypothesis that infected bulls could excrete BTV in their semen led to restrictions on international trade of ruminant semen and the establishment of measures to prevent BTV transmission by semen. However, neither the risk of BTV transmission by semen nor the effectiveness of these measures was estimated quantitatively. The objective of the study was to assess, in case of introduction of BTV into a bovine semen collection centre (SCC), both the risk of BTV transmission by bovine semen and the risk reduction achieved by the preventive measures available, by means of a stochastic risk assessment model. The model was applied to different scenarios, depending on for example the type of diagnostic test and the interval between the controls of donor bulls, or the rate of BTV spread within the SCC. Enzyme-linked immunosorbant assay (ELISA) controls of donor bulls every 60 days seemed to be an ineffective method for reducing the risk of BTV transmission in contrast to polymerase chain reaction (PCR) tests every 28 days. An increase in the rate of spread within the SCC resulted in a reduced risk of BTV transmission by semen. The storage of semen for 30 days prior to dispatch seemed to be an efficient way of reducing the risk of transmission by semen. The sensitivity analysis identified the probability of BTV shedding in semen as a crucial parameter in the probability of BTV transmission by semen. However, there is a great degree of uncertainty associated with this parameter, with significant differences depending on the BTV serotype.

In this thesis, a new model for the slow start phase based on the discrete evolutions of congestion window is developed, and we integrate this part into the improved TCP steady state model for a better prediction performance. Combining these short and steady state models, we propose an extensive stochastic model which can accurately predict the throughput and latency of the TCP connections as functions of loss rate, round-trip time (RTT), and file size. We validate our results through simulation experiments. The results show that our model?s predictions match the simulation results better than the Padhye and Cardwell's stochastic models, about 75% improvement in the accuracy of performance predictions for the steady state and 20% improvement for the short-lived TCP flows.

<p> The Volta River Authority (VRA) is responsible for the generation and transmission of power in Ghana. For this purpose, VRA owns and operates two hydroelectric generating stations (at Akosombo and Kpong) with a combined installed capacity of 1060 Kw. The Akosombo plant is served by the Lake Volta Reservoir. Prediction of inflows into the Volta Lake is one of the important functions of the reservoir management group.</p> <p>For this project, some of the more recent methods of mathematical modelling are investigated with a view to building a simple stochastic model which adequately represents and forecasts the Volta river average monthly flow. The Box-Jenkins family of models are employed in this exercise. A parsimonious model in the form of a seasonal autoregressive integrated moving average (SARIMA) model is arrived at which adequately models and forecasts the available data.</p> <p>The selected model is reasonably easy to set up, has few parameters to estimate and therefore making the updating of these parameters a relatively simple task.</p> / Thesis / Master of Engineering (MEngr)

Desenvolvemos um modelo estocástico da atividade elétrica de um neurônio motor do gânglio estomatogástrico de crustáceos, a partir de um modelo determinístico eletrofisiologicamente plausível. Com isso recuperamos características da dinâmica neural sempre observadas em neurônios isolados, tais como irregularidades nos padrões de disparos que não são reproduzidas pelo modelo determinístico original. Implementamos otimizações e simplificações no método numérico de simulação estocástica que permitiram rodar a simulação em tempo real para interagir modelos computacionais com neurônios biológicos, implementando sinapses artificiais entre eles. Por fim utilizamos o modelo e os métodos de simulação desenvolvidos para substituir neurônios do gânglio estomatogástrico e construir sistemas híbridos, que foram usados para verificar como ocorre a transmissão de informação entre neurônios biológicos e artificiais, quando a dinâmicas destes é estocástica ou determinística. / We developed a mathematical model of the electrical activity of a motor neuron from the stomatogastric ganglion of crustaceans. It was inspired on a previous existing deterministic model which is considered as electrophysiologically plausible in the recent literature. However, this deterministic model were not able to reproduce the irregular bursting behavior found in those biological neurons when isolated from the neural circuit. Our model, based on the microscopic stochastic behavior of the membrane ion channels, successfully reproduced the intrinsic irregular properties that were missing in the original deterministic model. To allow the real time performing of the stochastic model simulations we have to deal with some simplifications and to implement several optimizations that are also describe in detail. The real time version of our stochastic model was implemented in a dynamic clamp protocol to interface the computational model to real neurons. Finally, we applied the implemented versions of real time simulation and interfacing protocols to replace some biological bursting neurons of the stomatogastric ganglion. These hibrid neural networks were used to study how the information (diferent patterns of interspike intervals) is transmitted between biological and two types of artificial neurons: deterministic and stochastic.

Inventory management and pricing decisions based on quantitative models both in industrial practice and academic works often rely on minimizing expected cost or maximizing expected revenues or profits, which refers to the concept of risk-neutrality of the decision maker. Although many useful insights in operational problems can be obtained by such an approach, it is well understood that incorporating attitudes toward risk is an important lever for building new theories in other fields such as economics and finance. The level of risk associated with an investment might be as important as the expected gain from the investment. Hence, it is necessary to find appropriate measures of risk and the appropriate objectives related to or including these risk measures for inventory control & pricing problems. After the axiomatic foundation of coherent risk measures the application of risk measures to inventory models such as Conditional Value-at-Risk (CVaR) or convex combinations of mean and CVaR became popular. In our work we apply spectral risk measures to the single-period, single-item, linear cost inventory control & pricing problem (also known as newsvendor problem) and derive optimal policies. By doing so, we are able to unify results obtained so far in the literature under the common concept of spectral risk measures for the case of zero and non-zero shortage penalty cost. In particular, we show convexity results and structural properties for the inventory control and, under some assumptions, unimodality results as well as structural properties for the joint inventory & pricing problem. An extensive numerical analysis illustrates the findings. (author's abstract)

Hyperglycemia is prevalent in critical care, as patients experience stress-induced hyperglycemia, even with no history of diabetes. Hyperglycemia has a significant impact on patient mortality, outcome and health care cost. Tight regulation can significantly reduce these negative outcomes, but achieving it remains clinically elusive, particularly with regard to what constitutes tight control and what protocols are optimal in terms of results and clinical effort. Hyperglycemia in critical care is not largely benign, as once thought, and has a deleterious effect on outcome. Recent studies have shown that tight glucose regulation to average levels from 6.1–7.75 mmol/L can reduce mortality 17–45%, while also significantly reducing other negative clinical outcomes. However, clinical results are highly variable and there is little agreement on what levels of performance can be achieved and how to achieve them. A typical clinical solution is to use ad-hoc protocols based primarily on experience, where large amounts of insulin, up to 50 U/hr, are titrated against glucose measurements variably taken every 1–4 hours. When combined with the unpredictable and sudden metabolic changes that characterise this aspect of critical illness and/or clinical changes in nutritional support, this approach results in highly variable blood glucose levels. The overall result is sustained periods of hyper- or hypo- glycemia, characterised by oscillations between these states, which can adversely affect clinical outcomes and mortality. The situation is exacerbated by exogenous nutritional support regimes with high dextrose content. Model-based predictive control can deliver patient specific and adaptive control, ideal for such a highly dynamic problem. A simple, effective physiological model is presented in this thesis, focusing strongly on clinical control feasibility. This model has three compartments for glucose utilisation, interstitial insulin and its transport, and insulin kinetics in blood plasma. There are two patient specific parameters, the endogenous glucose removal and insulin sensitivity. A novel integral-based parameter identification enables fast and accurate real-time model adaptation to individual patients and patient condition. Three stages of control algorithm developments were trialed clinically in the Christchurch Hospital Department of Intensive Care Medicine. These control protocols are adaptive and patient specific. It is found that glycemic control utilising both insulin and nutrition interventions is most effective. The third stage of protocol development, SPRINT, achieved 61% of patient blood glucose measurements within the 4–6.1 mmol/L desirable glycemic control range in 165 patients. In addition, 89% were within the 4–7.75 mmol/L clinical acceptable range. These values are percentages of the total number of measurements, of which 47% are two-hourly, and the rest are hourly. These results showed unprecedented tight glycemic control in the critical care, but still struggle with patient variability and dynamics. Two stochastic models of insulin sensitivity for the critically ill population are derived and presented in this thesis. These models reveal the highly dynamic variation in insulin sensitivity under critical illness. The stochastic models can deliver probability intervals to support clinical control interventions. Hypoglycemia can thus be further avoided with the probability interval guided intervention assessments. This stochastic approach brings glycemic control to a more knowledge and intelligible level. In “virtual patient” simulation studies, 72% of glycemic levels were within the 4–6.1 mmol/L desirable glycemic control range. The incidence level of hypoglycemia was reduced to practically zero. These results suggest the clinical advances the stochastic model can bring. In addition, the stochastic models reflect the critical patients’ insulin sensitivity driven dynamics. Consequently, the models can create virtual patients to simulated clinical conditions. Thus, protocol developments can be optimised with guaranteed patient safety. Finally, the work presented in this thesis can act as a starting point for many other glycemic control problems in other environments. These areas include the cardiac critical care and neonatal critical care that share the most similarities to the environment studied in this thesis, to general diabetes where the population is growing exponentially world wide. Furthermore, the same pharmacodynamic modelling and control concept can be applied to other human pharmacodynamic control problems. In particular, stochastic modelling can bring added knowledge to these control systems. Eventually, this added knowledge can lead clinical developments from protocol simulations to better clinical decision making.

No description available.

Made available in DSpace on 2014-06-11T19:22:25Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-05-29Bitstream added on 2014-06-13T18:08:13Z : No. of bitstreams: 1 silva_ha_me_prud.pdf: 2618530 bytes, checksum: b2c909f5a51e515ca736f8c6a5a4def3 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Atualmente, o GNSS, em especial o GPS, é uma das tecnologias mais utilizadas para realizar posicionamento. Os modelos funcionais relacionados com as observações GNSS são mais conhecidos do que os modelos estocásticos, visto que o desenvolvimento destes últimos é mais complexo. Normalmente, no posicionamento GNSS são utilizados modelos estocásticos numa forma simplificada, com um modelo padrão, o qual assume que todas as medidas das observações GNSS têm a mesma variância e são estatisticamente independentes. Porém, atualmente os modelos estocásticos relacionados ao GNSS vêm sendo pesquisados com maior profundidade, por exemplo, considerando efeitos de cintilação ionosférica. Este efeito pode ser considerado na modelagem estocástica já que atualmente receptores GNSS permitem a extração de parâmetros de cintilação ionosférica. Além dessa, outro tipo de modelagem estocástica pode ser realizada, no caso, trata-se da consideração da variação dos ângulos de elevação dos satélites durante o rastreio dos dados. Sendo assim, nessa pesquisa foram desenvolvidos e analisados esses dois casos de modelagem estocástica, tanto no posicionamento relativo, quanto no absoluto (por ponto). No posicionamento relativo, ao se considerar a modelagem estocástica em função da cintilação ionosférica, os resultados atingiram melhorias em torno de 93,0% em relação à modelagem padrão. No processamento e análise foram utilizados dados GPS coletados no Norte da Europa, os quais estão sob condições de cintilação ionosférica. No posicionamento relativo considerando a modelagem estocástica em função dos ângulos de elevação dos satélites, as melhorias foram em torno de 89,2%. No caso do posicionamento por ponto, as melhorias em relação a modelagem estocástica padrão atingiram valores de aproximadamente 45,1% e 42,1% considerando, respectivamente... / Nowadays, the GNSS, especially the GPS, is one of the most used techniques to accomplish positioning. The functional models related with the GNSS observables are more known than the stochastic models, considering that the development of the last ones is more complex. Usually, they are used in a simplified form, as the standard model, which assumes that all the GNSS observable have the same variance and are statistically independent. However, the stochastic models are being investigated with more property, for example, considering the ionospheric scintillation effects. This effect can be considered in the stochastic modelling since now receivers GNSS allow the extraction of ionospheric scintillation parameters. Besides that, others stochastic modelling can be accomplished, e.g. considering the variation of the satellites elevation angles during the data tracking. Thus, in this dissertation it was investigated the two cases of stochastic modelling cited above, either in the relative or in the absolute positioning... (Complete abstract click electronic access below)

Desenvolvemos um modelo estocástico da atividade elétrica de um neurônio motor do gânglio estomatogástrico de crustáceos, a partir de um modelo determinístico eletrofisiologicamente plausível. Com isso recuperamos características da dinâmica neural sempre observadas em neurônios isolados, tais como irregularidades nos padrões de disparos que não são reproduzidas pelo modelo determinístico original. Implementamos otimizações e simplificações no método numérico de simulação estocástica que permitiram rodar a simulação em tempo real para interagir modelos computacionais com neurônios biológicos, implementando sinapses artificiais entre eles. Por fim utilizamos o modelo e os métodos de simulação desenvolvidos para substituir neurônios do gânglio estomatogástrico e construir sistemas híbridos, que foram usados para verificar como ocorre a transmissão de informação entre neurônios biológicos e artificiais, quando a dinâmicas destes é estocástica ou determinística. / We developed a mathematical model of the electrical activity of a motor neuron from the stomatogastric ganglion of crustaceans. It was inspired on a previous existing deterministic model which is considered as electrophysiologically plausible in the recent literature. However, this deterministic model were not able to reproduce the irregular bursting behavior found in those biological neurons when isolated from the neural circuit. Our model, based on the microscopic stochastic behavior of the membrane ion channels, successfully reproduced the intrinsic irregular properties that were missing in the original deterministic model. To allow the real time performing of the stochastic model simulations we have to deal with some simplifications and to implement several optimizations that are also describe in detail. The real time version of our stochastic model was implemented in a dynamic clamp protocol to interface the computational model to real neurons. Finally, we applied the implemented versions of real time simulation and interfacing protocols to replace some biological bursting neurons of the stomatogastric ganglion. These hibrid neural networks were used to study how the information (diferent patterns of interspike intervals) is transmitted between biological and two types of artificial neurons: deterministic and stochastic.