Dans ce travail nous abordons deux problèmes non résolus en Probabilité appliquée. Nous les approchons tous deux sous un angle nouveau, en utilisant des outils aussi variés que les chaînes de Markov, les mouvements Browniens, les transformations de Schwarz-Christoffel, les processus de Poisson et la théorie des temps d'arrêts optimaux. Problème de la ruine pour N joueurs Le problème de la ruine pour $N$ joueurs est un problème célèbre dont la solution pour $N=2$ est connue depuis longtemps. Nous l'abordons premièrement en toute généralité, en le modélisant comme un problème d'absorption pour une chaîne de Markov. Nous obtenons les distributions associées à ce problème et nous décrivons un algorithme (appelé {it folding algorithm}) permettant de diminuer considérablement le nombre d'opérations nécessaires à une résolution complète. Cette étude nous permet de mettre en avant un certain nombres de relations de récurrence satisfaites par les probabilités de ruines associées à chaque état de la chaîne de Markov. Nous étudions ensuite une version asymptotique du problème de la ruine pour 3 joueurs. Nous utilisons les propriétés d'invariance des mouvements Browniens par transformations conformes pour décrire une résolution de ce problème via les transformations de Schwarz-Christoffel. Cette méthode dépasse le cadre strict du problème de la ruine pour 3 joueurs et s'applique à d'autres problèmes de temps d'atteinte d'un bord par un mouvement Brownien. Problème de Robbins Ce problème s'inscrit dans le cadre de la théorie des temps d'arrêts optimaux. C'est un problème d'analyse séquentielle dans lequel un observateur examine $n$ variables aléatoires indépendantes de manière séquentielle et doit en sélectionner exactement une sans rappel. L'objectif est de déterminer une stratégie qui permette de minimiser le rang moyen de l'observation sélectionnée. Nous décrivons un modèle alternatif de ce problème, dans lequel le décideur observe un nombre aléatoire d'arrivées distribuées suivant un processus de Poisson homogène sur un horizon fixe $t$. Nous prouvons l'existence d'une stratégie optimale pour chaque horizon, et nous montrons que la fonction de perte associée à cette stratégie est uniformément continue sur $R$. Nous décrivons une fonction de perte restreinte qui permet d'obtenir une estimation de la valeur asymptotique du problème, et nous obtenons la valeur asymptotique associée à des stratégies spécifiques. Nous obtenons ensuite une équation intégro-diffférentielle sur la fonction de perte associée à la stratégie optimale. Finalement nous étudions les valeurs asymptotiques du problème et nous les comparons à celles du problème en temps discret. Nous concluons cette thèse en décrivant des stratégies spécifiques qui permettent d'obtenir des estimations sur le comportement asymptotique de la fonction de perte.

Monte Carlo sampling-based methods are frequently used in stochastic programming when exact solution is not possible. In this dissertation, we develop two sets of Monte Carlo sampling-based algorithms to solve classes of two-stage stochastic programs. These algorithms follow a sequential framework such that a candidate solution is generated and evaluated at each step. If the solution is of desired quality, then the algorithm stops and outputs the candidate solution along with an approximate (1 - α) confidence interval on its optimality gap. The first set of algorithms proposed, which we refer to as the fixed-width sequential sampling methods, generate a candidate solution by solving a sampling approximation of the original problem. Using an independent sample, a confidence interval is built on the optimality gap of the candidate solution. The procedures stop when the confidence interval width plus an inflation factor falls below a pre-specified tolerance epsilon. We present two variants. The fully sequential procedures use deterministic, non-decreasing sample size schedules, whereas in another variant, the sample size at the next iteration is determined using current statistical estimates. We establish desired asymptotic properties and present computational results. In another set of sequential algorithms, we combine deterministically valid and sampling-based bounds. These algorithms, labeled sampling-based sequential approximation methods, take advantage of certain characteristics of the models such as convexity to generate candidate solutions and deterministic lower bounds through Jensen's inequality. A point estimate on the optimality gap is calculated by generating an upper bound through sampling. The procedure stops when the point estimate on the optimality gap falls below a fraction of its sample standard deviation. We show asymptotically that this algorithm finds a solution with a desired quality tolerance. We present variance reduction techniques and show their effectiveness through an empirical study.

The discovery of carbon nanotubes by Iijima in 1991 has created a torrent of new research activities. Research on carbon nanotubes ranges from studying their fundamental properties, such as their electron band structure and plasma frequencies, to developing new applications, such as self-assembled nano-circuits and field emission displays. Robust models are now needed to enable a better understanding of the electronic response of carbon nanotubes. We use time-dependent density functional theory to derive a two-fluid two-dimensional (2D) hydrodynamic model describing the collective response of a multiwalled carbon nanotube with dielectric media embedded inside or surrounding the nanotube. We study plasmon hybridization of the nanotube system in the UV range, the stopping force for ion channelling, the dynamical image potential for fast ions, channelled diclusters and point dipoles, and the energy loss for ions with oblique trajectories. Comparisons are made of results obtained from the 2D hydrodynamic model with those obtained from an extension of the 3D Kitagawa model to cylindrical geometries.

Engineering design often requires the optimisation of multiple objectives, and becomes significantly more difficult and time consuming when the response surfaces are multimodal, rather than unimodal. A surrogate model, also known as a metamodel, can be used to replace expensive computer simulations, accelerating single and multi-objective optimisation and the exploration of new design concepts. The main research focus of this work is to investigate the use of a neural network surrogate model to improve optimisation of multimodal surfaces. Several significant contributions derive from evaluating the Cascade Correlation neural network as the basis of a surrogate model. The contributions to the neural network community ultimately outnumber those to the optimisation community. The effects of training this surrogate on multimodal test functions are explored. The Cascade Correlation neural network is shown to map poorly such response surfaces. A hypothesis for this weakness is formulated and tested. A new subdivision technique is created that addresses this problem; however, this new technique requires excessively large datasets upon which to train. The primary conclusion of this work is that Cascade Correlation neural networks form an unreliable basis for a surrogate model, despite successes reported in the literature. A further contribution of this work is the enhancement of an open source optimisation toolkit, achieved by the first integration of a truly multi-objective optimisation algorithm.

No description available.

A cornerstone in the theory of optimal stopping for the maximum process is a result known as Peskir’s maximality principle. It has proved to be a powerful tool to solve optimal stopping problems involving the maximum process under the assumption that the driving process X is a time-homogeneous diffusion. In this thesis we adapt Peskir’s maximality principle to allow for X a spectrally negative L´evy processes, thereby providing a general method to approach optimal stopping problems for the maximum process driven by spectrally negative L´evy processes. We showcase this by explicitly solving three optimal stopping problems and the capped versions thereof. Here capped version means a modification of the original optimal stopping problem in the sense that the payoff is bounded from above by some constant. Moreover, we discuss applications of the aforementioned optimal stopping problems in option pricing in financial markets whose price process is driven by an exponential spectrally negative L´evy process. Finally, to further highlight the applicability of our general method, we present the solution to the problem of predicting the time at which a positive self-similar Markov process with one-sided jumps attains its maximum or minimum.

A distância de visibilidade de parada deve ser garantida ao longo de toda a extensão de uma rodovia por questões de segurança. Elementos da seção transversal podem se tornar obstruções que interferem nas distâncias de visibilidade do projeto. Este é o caso do uso de barreiras ao invés de canteiros centrais em rodovias bidirecionais, especialmente ao longo de curvas à esquerda. Desta forma, este trabalho analisa o posicionamento de barreiras em cenários hipotéticos aclives planos e declives com uso de simulações gráficas tridimensionais. O afastamento lateral da barreira, em relação à pista de rolamento, foi definido em função de cada velocidade de projeto e de cada raio de curva horizontal analisados. Os diagramas gerados foram comparados com modelo de afastamento de objetos fixos em curvas horizontais, presente como recomendações em manuais nacionais. As diferenças encontradas indicam a viabilidade da metodologia utilizada, em que o projeto foi considerado como um todo, o qual se desenvolve tridimensionalmente. / Stopping Sight Distance must be guaranteed throughout of a highway for safety reasons. However, cross section elements can become obstructions which interfere on design sight distances. This occurs when barriers are used instead of medians on bidirectional highways, especially along left curves. Therefore, this paper analyzes the barriers placement on hypothetical scenarios upgrades, plans and downgrades using three-dimensional graphics simulations. The lateral offset of the barrier in relation to the roadway was defined according to each design speed and each radius of the horizontal curve analysis. For each scenario were generated diagrams, which use compared with offset model of fixed objects on horizontal curves presents as recommendation in national manuals. The differences indicate the viability of the methodology used, where the project was considered as a whole, which develops three-dimensionally.

The main contribution of this thesis is to derive the properties and present a closed from solution of the exotic options under some specific types of Levy processes, such as American put options, American call options, British put options, British call options and American knock-out put options under either double exponential jump-diffusion processes or one-sided exponential jump-diffusion processes. Compared to the geometric Brownian motion, exponential jump-diffusion processes can better incorporate the asymmetric leptokurtic features and the volatility smile observed from the market. Pricing the option with early exercise feature is the optimal stopping problem to determine the optimal stopping time to maximize the expected options payoff. Due to the Markovian structure of the underlying process, the optimal stopping problem is related to the free-boundary problem consisting of an integral differential equation and suitable boundary conditions. By the local time-space formula for semi-martingales, the closed form solution for the options value can be derived from the free-boundary problem and we characterize the optimal stopping boundary as the unique solution to a nonlinear integral equation arising from the early exercise premium (EEP) representation. Chapter 2 and Chapter 3 discuss American put options and American call options respectively. When pricing options with early exercise feature under the double exponential jump-diffusion processes, a non-local integral term will be found in the infinitesimal generator of the underlying process. By the local time-space formula for semi-martingales, we show that the value function and the optimal stopping boundary are the unique solution pair to the system of two integral equations. The significant contributions of these two chapters are to prove the uniqueness of the value function and the optimal stopping boundary under less restrictive assumptions compared to previous literatures. In the degenerate case with only one-sided jumps, we find that the results are in line with the geometric Brownian motion models, which extends the analytical tractability of the Black-Scholes analysis to alternative models with jumps. In Chapter 4 and Chapter 5, we examine the British payoff mechanism under one-sided exponential jump-diffusion processes, which is the first analysis of British options for process with jumps. We show that the optimal stopping boundaries of British put options with only negative jumps or British call options with only positive jumps can also be characterized as the unique solution to a nonlinear integral equation arising from the early exercise premium representation. Chapter 6 provides the study of American knock-out put options under negative exponential jump-diffusion processes. The conditional memoryless property of the exponential distribution enables us to obtain an analytical form of the arbitrage-free price for American knock-out put options, which is usually more difficult for many other jump-diffusion models.

No description available.

No presente trabalho é apresentado o Teste de Omissões Voluntárias (Square-Skipping Test, SST), uma versão de papel e lápis da tarefa computadorizada do sinal inibitório. Na primeira parte do trabalho, são relatados estudos que utilizaram uma tarefa computadorizada do sinal inibitório com estímulos excitatórios e inibitórios apresentados visualmente em um procedimento lateralizado. As estratégias de esperar o sinal inibitório foram controladas com sucesso mediante o controle "on-line" da estabilidade dos tempos de reação ao sinal excitatório. Um dos objetivos foi elucidar algum possível fator comum subjacente ao desempenho na tarefa do sinal inibitório e no Teste da tarefa Dupla. Os tempos de reação ao sinal inibitório não foram afetados pela lateralização, enquanto que os tempos de reação ao sinal excitatório direito foram os mais rápidos. Esta vantagem, a qual parece envolver especialização hemisférica e comunicação interhemisférica, correlacionou com a perda no desempenho da tarefa de box-crossing quando combinada com a tarefa verbal no Teste da Tarefa Dupla. A diferença Parte B-menos-Parte A do Trail Making Test correlacionou com os tempos de reação simples. Os resultados também sugerem a associação entre o tempo de reação simples e funções executivas. Foi descartada uma assimetria no sentido do deslocamento da atenção entre hemicampos para explicar a vantagem dos tempos de reação ao sinal excitatório direito. O tempo de reação simples parece ser uma medida de capacidade executiva. A comparação do desempenho de adultos idosos e jovens, medido pela tarefa computadorizada, demostrou que o controle inibitório não foi afetado de forma significativa pela idade. Na segunda parte do trabalho, é apresentado o SST, o qual permite obter de forma prática e rápida, medidas da habilidade inibitória e outras capacidades executivas tais como a flexibilidade cognitiva, a atenção concentrada e a velocidade na busca visual. O SST foi validado mediante a comparação com o desempenho na tarefa computadorizada do sinal inibitório. A execução do SST requer marcar com ‘Xs’ quadradinhos alinhados em um caminho irregular impressos em uma folha A4 (Parte D), sendo que nas Partes A, B e C devem-se omitir alguns quadradinhos indicados. Na terceira tentativa do SST deve ser escrita a seqüência de dígitos ‘1, 2, 3’. A correlação com o teste computadorizado do sinal inibitório sugeriu que o controle inibitório seria medido pela Parte D preenchida com a seqüência de dígitos (Parte D3). A idade não afetou de forma significativa o desempenho na Parte D3. O fator idade parece afetar seletivamente o desempenho nas diferentes partes do SST; p. ex. na Parte A1, que correlacionou com o coeficiente de atenção concentrada do Teste de Toulouse-Pièron. Para evitar os efeitos da prática sobre o desempenho no SST, recomenda-se a execução do Teste da Tarefa Dupla antes da execução do SST, e de preferência na mesma sessão experimental. / The present study aims to contribute to the understanding of the inhibitory ability, within the framework of the neuropsychology. The objective was to develop a paper-and-pencil test to assess the ability to stop an action in a simple and rapid way. A computerized stop signal task was used to validate the test. In the first part of this work, studies that involved the computerized stop signal task are presented. The result of these studies allowed to raise some theoretical issues. The paper-and-pencil test is presented in the second part of this work. In the Experiment 1 the aim was to control experimentally the strategy of waiting for the stop-signal on a lateralized stop signal task, by means of an algorithm, which controlled, on-line, the variation of response latencies for the go-signal (GSRT). Thirty-four healthy volunteers participated in this study. The GRST of the group that performed the task without the algorithm were significantly higher than the GSRT of the group that performed the task with the algorithm, whereas the stop-signal reaction times did not reach significant differences between groups. This procedure provided more stable reaction times throughout the task, and shifted the probability of responding on stop-trials from 0.364 to 0.479. The Experiment 2 studied the relationship between reaction time, laterality, and executive functions were examined by employing two computerized tasks with lateralized visual stimuli. Simple reaction time (SRT) was correlated with the Part B-minus-A difference of Trail Making Test (TMT). No significant difference was found between left and right SRT. Reaction times for left go-signals of the Stop-task were longer than reaction times for right go-signals. The ratio of left go-signal-minus left SRT to right go-signal-minus-right SRT was correlated with the loss in the visuospatial component when it was combined with a concurrent verbal task in the Dual-Task Test. Results suggest association between SRT and executive functions, and the involvement of hemispheric specialization and interhemispheric transfer in both, the stop signal task and the Dual-Tasks Test. Results from Experiment 3 permit to discard the possibility that the observed right visual field advantage observed was due to the orienting of attention across hemifields. The left GSRT were significantly slower than right GSRT. The right GRST advantage was not due to an attentional shift between left and right visual hemifields. In the Experiment 4, the stopping ability of older people in the computerized stop task was explored. There were no significant differences between the stopping ability of older and younger adults. The Square-skipping Test (SST) a paper-an-pencil version of the stop signal computerized task. is described in the second part of this study. The SST is divided in four parts. The effect of the administration of the different parts of the SST was studied in Experiment 5. The results allow for the use of the four parts in the same trial, since there was no effect of order of administration. In Experiment 6 it was studied the effect of placing a digit sequence on the third trial of the test, instead of the X’s. It seems that a greater degree on the inhibitory ability is necessary to perform the task with the sequence "1, 2, 3", than with the sequence "3, 2, 1". Thus, the sequence "1, 2, 3" was used in the final version of the SST. The practice effects of the Dual-Task Test on the SST was studied in Experiment 7. The interaction Group x Trial showed a general decrease on the performance of participants without previous practice in the Dual-task Test, contrasting with the performance of participants with within-session practice, which showed a clear digit sequence load effect. The aim of Experiment 8 was to know possible aging effects in the performance of SST. A general decrease was observed in the performance of older adults compared with performance of young adults; the interaction Group x Trial showed that the slope of the curves were different. The performance in SST is significantly affected by age. Performance in SST correlated with performance in the stop signal and the SRT tasks, respectively. Performance in SST also correlates with TMT, with the visuospatial component of the mu index of the Dual-task and with the attention coefficient of the Toulouse-Pièron Test. The best predictor of the stopping ability was the performance on the Part D with the digit sequence (Part D3). Thus, SST seems to be a useful neuropsychological tool for the assessment of several executive functions, including the stopping ability, mental flexibility, speed for visual search and focused attention.