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Thesis (Ph. D.)--School of Computing and Engineering. University of Missouri--Kansas City, 2008. / "A dissertation in computing networking and telecommunications networking." Advisor: Appie van de Liefvoort. Typescript. Vita. Title from "catalog record" of the print edition Description based on contents viewed Feb. 6, 2009. Includes bibliographical references (leaves 85-89). Online version of the print edition.

Thesis (Ph. D.)--University of Washington, 1995. / Vita. Includes bibliographical references (leaves [188]-192).

Made available in DSpace on 2014-06-11T19:23:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-12-13Bitstream added on 2014-06-13T18:09:47Z : No. of bitstreams: 1 catalao_ab_me_ift.pdf: 811288 bytes, checksum: d4e34c59801bd92233bc9f26884a19ab (MD5) / Neste trabalho estudamos a calibração de opções de câmbio no mercado brasileiro utilizando o processo estocástico proposto por Heston [Heston, 1993], como uma alternativa ao modelo de apreçamento de Black e Scholes [Black e Scholes,1973], onde as volatilidades implícitas de opções para diferentes preços de exercícios e prazos são incorporadas ad hoc. Comparamos dois métodos de apreçamento: o método de Carr e Madan [Carr e Madan, 1999], que emprega transfomada rápida de Fourier e função característica, e expansão assintótica para baixos valores de volatilidade da variância. Com a nalidade de analisar o domínio de aplicabilidade deste método, selecionamos períodos de alta volatilidade no mercado, correspondente à crise subprime de 2008, e baixa volatilidade, correspondente ao período subsequente. Adicionalmente, estudamos a incorporação de swaps de variância para melhorar a calibração do modelo / In this work we study the calibration of forex call options in the Brazilian market using the stochastic process proposed by Heston [Heston, 1993], as an alternative to the Black and Scholes [Black e Scholes,1973] pricing model, in which the implied option volatilities related to di erent strikes and maturities are incorporated in an ad hoc manner. We compare two pricing methods: one from Carr and Madan [Carr e Madan, 1999], which uses fast Fourier transform and characteristic function, and asymptotic expantion for low values of the volatility of variance. To analyze the applicability of this method, we select periods of high volatility in the market, related to the subprime crisis of 2008, and of low volatility, correspondent to the following period. In addition, we study the use of variance swaps to improve the calibration of the model

Within the context of rank-based interacting particle systems, we study the fluctuations in a symmetric ensemble around its stable distribution. This system is inspired by the classic Atlas model but represents its opposite pole since both the highest- and lowest-ranked particles will have non-zero drifts. In the first part of the dissertation, we derive a fine asymptotic analysis that includes a Law of Large Numbers. The lack of monotonicity of the ensemble requires that we develop alternative tools to those traditionally used in the analysis of the Atlas model. In the second part of the dissertation, we characterize the system’s fluctuations and show that, as the number of particles goes to infinity, they converge weakly to the mild solution of the Additive Stochastic Heat Equation on the real line with a symmetric initial condition. To establish this result, we use the technique proposed by Dembo and Tsai, 2017, where the Empirical Measure Process is used as a proxy for the ensemble’s fluctuations. We expect that a combination of our work, and the available knowledge about the Atlas model, could help draw a full picture of how a finite rank-based interacting particle system with a general drift structure fluctuates around its stationary distribution as the number of particles goes to infinity, a long-standing open question in the field.

In this dissertation, we investigate a very interesting class of quasi-linear stochastic partial differential equations. The main purpose of this article is to prove an existence result for such type of stochastic differential equations with non-standard growth conditions. The main difficulty in the present problem is that the existence cannot be easily retrieved from the well known results under Lipschitz type of growth conditions [42]. / Dissertation (MSc)--University of Pretoria, 2010. / Mathematics and Applied Mathematics / unrestricted

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The main objective of this study is to analyze the impact of the stochastic renewable distributed generation (DG) system on the urban distribution network. Renewable DG systems, particularly photovoltaic (PV) systems, dispersed on the distribution network may, in spite of their relatively small individual capacities, change the behavior of such a network. Therefore, this study (1) developed tools and algorithms useful for planning, designing, and operating such a network, (2) addressed some of the issues in the analysis of the impact of renewable DG systems on such a network, and (3) designed a framework for streamlining the future development and the smooth integration of renewable DG systems into the urban distribution network. For this purpose, in Task 1, using the backward and forward sweep method implemented in MATLAB, this study developed an algorithm for three-phase power flow that models power system components, including distribution systems, transformers, and PV systems. To model the influence of the inherent uncertainty of the input, the location, and the capacity of the PV system, this study implemented a stochastic simulation algorithm combined with the power-flow algorithm. It also accelerated the stochastic algorithm using a method of variance reduction, including importance sampling, and the sampling of representative clusters and extreme points, which reduced the extremely heavy computational burden that the stochastic simulation inevitably imposed. Then this study analyzed inherent uncertainties such as the inputs, the locations, and the capacities of residential PV systems stochastically installed on urban distribution networks by performing several stochastic simulations. In Task 2, this study developed a genetic algorithm in MATLAB that solves an optimization problem that maximizes the reliability (or minimizes the frequency and the duration of failure) of urban distribution networks enhanced by protection devices (i.e., the recloser, the fuse, and the switch) and renewable DG. Using the backward and forward method, this study implemented an analytical method that simulates all possible permanent and transient faults and evaluated the reliability of an urban distribution network housing a combination of fuses, switches, reclosers, and DG systems. Then it analyzed the impact of both the DG system, including the effect of the islanded operation of the DG system, and the protection device, on the reliability of the urban distribution network. The objective of Task 3 of this study was to present a useful method for analyzing the impact of geographically dispersed DG systems, particularly PV systems, on statewide and nationwide power grids. Using the methods of Lagrangian optimization and hydrothermal coordination, this study developed an algorithm for environmentally constrained generation resource allocation that minimizes both fuel costs and ecological impact, including the cost and the impact of water consumption. Then, this study (1) analyzed, as an example of the statewide power grid of the future, the power system of the state of Georgia in 2010, (2) modeled the load consumption and the water inflow of the power system, (3) synthesized third-order power output functions for costs, emissions, and water consumption from actual heat-rate data, and (4) estimated the power output of PV systems geographically dispersed throughout the state and hydroelectric resources of the state in hourly intervals. Lastly, it performed simulations for the generation resource allocation of the power system in hourly and minute intervals.

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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