Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: a) increase the efficiency of the portfolio optimization process, b) implement large-scale optimizations, and c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH).

[pt] Este trabalho propõe um novo modelo estocástico para o número diário de negócios com ações do mercado de capitais brasileiro. O modelo, que denominamos ZINB-HF (Zero-Inflated Negative Binomial Harvey-Fernandes), é uma extensão do modelo de uma escala local para dados de contagem. Nesse modelo, o número diário de negócios segue uma distribuição binomial negativa com relação serial. A distribuição binomial negativa é gerada através de três modelos microestruturais independentes do processo de negociação. O principal deles baseia-se no conceito de rupturas aleatórias no processo gerador dos retornos, que ocorrem num referencial de tempo alternativo, definido pelas próprias ocorrências de negócios. O segundo modelo microestrutural sugerido para justificar o uso da binomial negativa remete ao conceito de heterogeneidade não-observada nas periodicidades de negociação por parte dos agentes de mercado. O terceiro remete ao conceito de contágio positivo devido a um processo auto-reforçador da liquidez de uma ação. A distribuição binomial negativa autocorrelatada do modelo de escala local é suposta zero-inflada, isto é, a probabilidade de zero negócios em um dia qualquer é maior do que a distribuição binomial negativa pura indicaria, devido à existência de suspensões forçadas na negociação. O modelo ZINB-HF proposto é usado como processo direcionador dos retornos diários da ação, no contexto de deformação temporal. O trabalho conclui com um estudo de caso com uma ação representativa do mercado brasileiro. / [en] This thesis proposes a new stochastic model for the daily number of transactions with stocks in the Brazilian capital market. The model, which we call ZINB-HF (Zero – Inflated Negative Binomial Harvey- Fernandes), is an extension of a local scale model for count data. In it, the daily number of transactions follows a serially correlated negative binomial distribution. The negative binomial is generated through three independent microstructural models of the transaction process. The main model is based on the concept of random ruptures in the returns generating process, which occur in an alternative time frame of reference, defined by the transactions themselves. The second microstrutural model suggested, to justify the usage of a negative binomial points to the concept of non observed heterogeneity in the frequency of trading by market agents. The third one is based on the concept of positive contagion related to a self-reinforcing process of liquidity on the stock. The serially correlated negative binomial of the local scale model is supposed zero inflated, which means that the probability of zero transactions in any day is larger than indicated by a pure negative binomial, due to the existence of forced breaks in trading. The proposed ZINB-HF model is used as a directing process of daily returns of the stock, in the framework of a time deformation model. The work concludes with a case study a representative Brazilian stock.

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Grinding is a critical manufacturing process and is often the only alternative when producing precision components or when machining brittle materials such as ceramics. Characterizing and modeling the surface finish in the grinding process is a difficult task due to the stochastic nature of the size, shape and spatial distribution of abrasive grains that make up the surface of grinding wheels. Since the surface finish obtained in grinding is a direct function of the wheel surface topography, which is conditioned by a single point dressing process, understanding the effects of dressing parameters on the wheel topography is essential. Therefore, the main objectives of this thesis are: 1) to experimentally characterize the three-dimensional surface topography of a conventional grinding wheel including attributes such as the abrasive grain height distribution, grain geometry and spacing parameters and their respective statistical distributions, 2) to determine the effects of single point dressing conditions on the three-dimensional wheel surface topography parameters and their distributions, 3) to model and simulate the three-dimensional wheel surface topography, and 4) to experimentally validate the wheel topography model. In this research, new and existing characterization methods are used to characterize the wheel surface and the individual abrasive grains. The new techniques include the use of X-ray micro-tomography (μCT) to obtain a better understanding of the grinding wheel's internal micro-structure, and a focus variation based optical measurement method and scanning electron microscopy to characterize previously ignored attributes such as the number of sides and aspect ratio of individual grains. A seeded gel (SG) vitrified bond conventional grinding wheel is used in the study. A full factorial design of single point wheel dressing experiments is performed to investigate the effects infeed and lead dressing parameters on the grinding wheel surface topography. A custom wheel indexing apparatus is built to facilitate precision relocation of the grinding wheel surface to enable optical comparison of the pre- and post-dressing wheel surface topography to observe wheel surface generation mechanisms such as macro-fracture and grain dislodgement. Quantitative descriptions of how each dressing parameter affects the wheel surface characteristics are given in terms of the wheel surface roughness amplitude parameters (Sp, Ssk, Sku) and areal and volume parameters (Spk, Sk, Vmp, Vmp, Vvc, Smr1) derived from the bearing area curve. A three-dimensional wheel topography simulation model that takes as input the abrasive grain height distribution and the statistical distributions for the various abrasive grain geometry parameters is developed and experimentally validated. The results of wheel characterization studies show that the actual abrasive grain height distribution in the SG wheel follows a beta distribution. The μCT work shows that the abrasives are polyhedral in shape, as opposed to the spherical or conical shapes commonly assumed in grinding literature. Grain spacing is found to follow a beta distribution while the number of sides of the grain and the grain aspect ratio are found to follow the gamma and the Weibull distribution, respectively. The results of the dressing study show that the lead dressing parameter has the strongest effect on wheel topography. Using statistical distributions for the key parameters (e.g. grain height, number of sides, grain spacing), a stochastic three-dimensional model is developed to simulate the wheel surface topography under different dressing conditions. The resulting model is shown to yield realistic results compared to existing models mainly due the fact that additional abrasive grain geometry parameters and more realistic assumptions of the different grain attributes are used in the model. It is shown that the model follows the overall wheel surface topography trends during dressing but has difficulty in accurately simulating some of the wheel characteristics under specific dressing conditions. The thesis then concludes with a summary of the main findings and possible future research avenues including extending the model to rotary dressing and simulation of wheel-workpiece interaction.

Dropped objects are among the top ten causes of fatalities and serious injuries in the oil and gas industry. Objects may be dropped during lifting or any other offshore operation. Concerns of health, safety, and the environment (HSE) as well as possible damages to structures require the prediction of where and how a dropped object moves underwater. This study of dropped objects is subdivided into three parts. In the first part, the experimental and simulated results published by Aanesland (1987) have been successfully reproduced and validated based on a two-dimensional (2D) theory for a dropped drilling pipe model. A new three-dimensional (3D) theory is proposed to consider the effect of axial rotation on dropped cylindrical objects. The 3D method is based on a modified slender body theory for maneuvering. A numerical tool called Dropped Objects Simulator (DROBS) has been developed based on this 3D theory. Firstly, simulated results of a dropped drilling pipe model using a 2D theory by Aanesland (1987) are compared with results from 3D theory when rolling frequency is zero. Good agreement is found. Further, factors that affect the trajectory, such as drop angle, normal drag coefficient, binormal drag coefficient, and rolling frequency are systematically investigated. It is found that drop angle, normal drag coefficient, and rolling frequency are the three most critical factors determining the trajectories. In the second part, a more general three-dimensional (3D) theory is proposed to physically simulate the dynamic motion of a dropped cylindrical object underwater with different longitudinal center of gravity (LCG). DROBS has been further developed based on this 3D theory. It is initially applied to a dropped cylinder with LCG = 0 (cylinder #1) falling from the surface of calm water. The calculated trajectories match very well with both the experimental and numerical results published in Aanesland (1987). Then DROBS is further utilized to simulate two dropped cylinders with positive LCG (cylinder #2) and negative LCG (cylinder #3) in Chu et al. (2005), respectively. The simulated results from DROBS show a better agreement with the measured data than the numerical results given in Chu et al. (2005). This comparison again validates and indicates the effectiveness of the DROBS program. Finally, it’s applied to investigate the effects of varying LCG on the trajectory and landing points. Therefore, the newly developed DROBS program could be used to simulate the distribution of landing points of dropped cylindrical objects, as is very valuable in the risk-free zone prediction in offshore engineering. The third part investigates the dynamic motion of a dropped cylindrical object under current. A numerical procedure is developed and integrated into Dropped Objects Simulator (DROBS). DROBS is utilized to simulate the trajectories of a cylinder when dropped into currents from different directions (incoming angle at 0o; 90o; 180o; and 270o) and with different amplitudes (0m/s to 1.0m/s). It is found that trajectories and landing points of dropped cylinders are greatly influenced by currents. Cylinders falling into water are modeled as a stochastic process. Therefore, the related parameters, including the orientation angle, translational velocity and rotational velocity of the cylindrical object after fully entering the water, is assumed to follow normal distributions. DROBS is further used to derive the landing point distribution of a cylinder. The results are compared to Awotahegn (2015) based on Monte Carlo simulations. Then the Monte Carlo simulations are used for predicting the landing point distribution of dropped cylinders with drop angles from 0o to 90o under the influence of currents. The plots of overall landing point distribution and impact energy distribution on the sea bed provide a simple way to indicate the risk-free zones for offshore operation.

La modélisation du sous-sol est un outil indispensable pour décrire, comprendre et quantifier les processus géologiques. L'accès au sous-sol et son observation étant limités aux moyens d'acquisition, la construction de modèles tridimensionnels du sous-sol repose sur l'interprétation de données éparses à résolution limitée. Dans ce contexte, de nombreuses incertitudes affectent la construction de tels modèles, dues aux possibles biais humains cognitifs lors de l'interprétation, à la variabilité naturelle des objets géologiques et aux incertitudes intrinsèques des données utilisées. Ces incertitudes altèrent la prédictibilité des modèles et leur évaluation est donc nécessaire afin de réduire les risques économiques et humains liés à l'utilisation des modèles. Le travail de thèse s'est déroulé dans le cadre plus spécifique des incertitudes sur les structures géologiques. Les réponses apportées sont multiples : (1) une méthode stochastique de génération de modèles structuraux à géométrie et topologie changeantes, combinant une connaissance a priori des structures géologiques aux données interprétées, a été développée ; (2) le réalisme géologique des structures modélisées est garanti grâce à la modélisation implicite, représentant une surface par une équipotentielle d'un champ scalaire volumique ; (3) la description des failles en un nombre restreint de paramètres incertains a permis d'aborder la modélisation inverse, ce qui ouvre la voie vers l'assimilation de données géophysiques ou d'écoulement fluides grâce à des méthodes bayesiennes / Subsurface modeling is a key tool to describe, understand and quantify geological processes. As the subsurface is inaccessible and its observation is limited by acquisition methods, 3D models of the subsurface are usually built from the interpretation of sparse data with limited resolution. Therefore, uncertainties occur during the model building process, due to possible cognitive human bias, natural variability of geological objects and intrinsic uncertainties of data. In such context, the predictability of models is limited by uncertainties, which must be assessed in order to reduce economical and human risks linked to the use of models. This thesis focuses more specifically on uncertainties about geological structures. Our contributions are : (1) a stochastic method for generating structural models with various fault and horizon geometries as well as fault connections, combining prior information and interpreted data, has been developped ; (2) realistic geological objects are obtained using implicit modeling that represents a surface by an equipotential of a volumetric scalar field ; (3) faults have been described by a reduced set of uncertain parameters, which opens the way to the inversion of structural objects using geophysical or fluid flow data by baysian methods

In this thesis, we consider the trajectory planning of an autonomous vehicle to cross an intersection within a given time interval. The vehicle communicates its sensordata to a central coordinator which then computes the trajectory for the given time horizon and sends it back to the vehicle. We consider a realistic scenario in which the communication links are unreliable, the evolution of the state has noise (e.g., due to the model simplification and environmental disturbances), and the observationis noisy (e.g., due to noisy sensing and/or delayed information). The intersection crossing is modeled as a chance constraint problem and the stochastic noise evolution is restricted by a terminal constraint. The communication impairments are modeled as packet drop probabilities and Kalman estimation techniques are used for predicting the states in the presence of state and observation noises. A robust sub-optimalsolution is obtained using convex optimization methods which ensures that the intersection is crossed by the vehicle in the given time interval with very low chance of failure.

Os silos verticais são estruturas com elevado índice de deformações excessivas e ruptura causados, principalmente, pelo desconhecimento da variabilidade nas pressões devidas ao produto armazenado. O objetivo deste trabalho é apresentar um estudo teórico, numérico e experimental das pressões exercidas pelos produtos armazenados granulares nas paredes de silos esbeltos, com a proposta da incorporação de parâmetros com propriedades estocásticas, nos modelos de pressões apresentados na literatura. Os parâmetros mais relevantes dos modelos de pressões foram ajustados aos dados experimentais obtidos em um silo-piloto, utilizando a técnica de estimação de parâmetros por máxima verossimilhança (EMV), e, para isso, foram empregados os algoritmos genéticos (AGs) como procedimento de otimização. As avaliações experimentais no silo-piloto foram conduzidas com três produtos: soja, milho e ração. Com as variabilidades dos parâmetros dos modelos de pressões encontrados nos experimentos, a confiabilidade estrutural dos silos verticais metálicos cilíndricos de chapas onduladas e fundo plano foi avaliada por meio da técnica de simulação de Monte Carlo (SMC). Os resultados mostraram que os modelos de pressões de Janssen (1895) e de Jenike et al. (1973) podem ser utilizados para o cálculo das pressões com as variabilidades dos parâmetros representadas pela distribuição lognormal. A avaliação da probabilidade de falha para este sistema está acima dos limites recomendados internacionalmente, indicando que atenção especial deve ser dada aos projetos de silos verticais esbeltos. / Vertical silos are structures with a large number of deformations and failures mainly due to misunderstanding of pressure variability of the storage products. The aim of this work is theoretical, numerical and experimental study of wall pressure in slender silos with the incorporation of stochastic properties of the parameters in pressures models used in the international literature. The most relevant parameters of the pressure models were adjusted to the experimental data obtained from a pilot-silo using maximum likelihood function, and for this purpose, genetic algorithms (GA) were used in the optimization procedure. The experimental evaluation in pilot-silo was conducted with three different bulk solids, which are: maize, soy and animal feed mixture. With the pressures models parameters, the structural reliability of flat bottom corrugated cylindrical steel silos with was evaluated using Monte Carlo simulation (SMC) to simulate a stochastic process. The results showed that Janssen (1895) and Jenike et al. (1973) pressure models can be used to evaluate the pressures with the parameters uncertainties modeled to lognormal distributions. The reliability index determined in this structural system was less than international recommended values for the design of slender silos.

Antibiotic-resistant bacteria(ARB) is causing increased health risk and cost to society. Mathematical models have been developed to study the transmission of resistant bacteria and the efficacy of preventive measures to slow its spread within a hospital setting. The majority of these models have assumed a constant total hospital population with the admission and discharge rates being equal throughout the duration. But a typical hospital population varies from day to day and season to season. In this thesis, we apply variable admission and discharge daily rates to existing deterministic and stochastic models which examine the transmission of single and dual resistant bacteria. We perform stability and equilibrium analyses as well as a sensitivity analysis on the resulting model..

Theoretical modeling of biological response to radiation describes qualitatively and quantitatively the results of radiobiological effects at the molecular, chromosomal, and cellular level. The repair-misrepair (RMR) model is the radiobiological model chosen for our study. It models deoxyribonucleic acid (DNA) damage formation and lesion repair through linear and quadratic processes. Double strand breaks (DSB) are a critical lesion in DNA. With increasing LET, the number of DSB per track traversing the cell nucleus increases. Using a compound Poisson process (CPP), we describe DNA damage formation. Three models were considered: a simple CPP using constant LET, a CPP using a chord length distribution, and a CPP using specific energy distribution. In the two first cases, and for low LET radiation the initial distribution of DSB was well approximated by a Poisson distribution, while for high LET radiation the initial distribution of DSB deviated slightly from a Poisson distribution. In the last case, DSB distribution was much broader than a pure Poisson distribution. Datasets from the literature for seven human cell lines, exhibiting various sensitivities to radiation were analyzed. We compared stochastic, CPP, and CPP using chord length distribution, with deterministic RMR models. For low LET radiation and at high dose rates the stochastic survival results agree well with the deterministic survival results. Also the stochastic model allows for non-linearity at low doses due to the accumulation of sub-lethal damage. At low dose rates deterministic results overestimate the surviving fraction compared to stochastic results. For high LET radiation stochastic and deterministic survival results agree. Stochastic survival results using specific energy distribution diverged from deterministic results by underestimating the surviving fraction at low and high LET radiation. The dose rate sparing curve, representing surviving fraction at a dose of 10Gy vs. dose rate shows that deterministic survival results are consistent with stochastic survival results, using CPP, or CPP with chord length distribution, for low and high dose rate values. Compared to deterministic aspects of DNA damage formation we concluded that stochastic aspects of DNA damage formation and repair using CPP or CPP with chord length distribution are not as prominent as reported in the earlier studies.