國內外對BOT實質選擇權之研究，大多集中於BOT主體本身所隱含之各種選擇權價值，鮮少論及BOT附屬事業之選擇權價值。惟因交通運輸BOT主體之自償率往往偏低，故須以保證最小運量或特許經營附屬事業等方式，來吸引潛在投資者。附屬事業對整個BOT計畫價值的影響頗大，如何針對其選擇權之價值加以分析為本研究的主要課題。個案將以台灣南北高速鐵路計畫為例，對其附屬事業之放棄選擇權加以探討。 本研究將主要探討下列課題，並提出研究結果： 一、有限差分法及蒙地卡羅模擬法計算選擇權價值，其間之差異？本 文利用有限差分法及蒙地卡羅模擬法來各別求算BOT 附屬事業的 放棄選擇權價值，一來了解 BOT 附屬事業的放棄選擇權價的大 小，二來比較有限差分法及蒙地卡羅模擬法兩者間的差異。 二、BOT附屬事業的放棄選擇權是否受主體事業的經營績效所影響？ 三、BOT附屬事業是否須考量履約保證金之設計？ 四、BOT主體決定經營或放棄時，是否會影響其附屬事業之放棄選擇 權價值？ 本研究係以蒙地卡羅模擬法及有限差分法單獨估計台灣南北高速鐵路附屬事業之放棄選擇權價值，並建立運輸主體與附屬事業間價值的關聯，再以蒙地卡羅模擬法作更精確的估算。另使用單因子變異數分析及Tukey's Multiple Comparison Method之統計方法，驗證BOT主體與其附屬事業選擇權間之相關性，期能有助於日後BOT計畫之參與者評估及決策使用。 / The study of the Real Option Analysis (ROA) thesis of BOT generally focus is on the principal parts of the project only, rarely is considered the option of ancillary business of BOT. Because the self-liquidation-ratio of the transportation of BOT is low, it needs the government financial support (minimum traffic guarantee or revenue enhancements) to attract the interest of intended investors. The influence of the ancillary business of BOT is huge, so how to evaluate the option is the big issue of thesis. The case focus on the Taiwan High Speed Rail BOT project, and will study the option value of it’s ancillary business. Thesis will discuss the following issues, and develop the result of study. 1.The calculation difference between Monte Carlo Simulation & Finite Difference Method to work out option value, Thesis will use the Monte Carlo Simulation & Finite Difference Method to work out the abandon option value of ancillary business of BOT. To get the abandon option value and compare the calculation difference between Monte Carol Simulation & Finite Difference Method. 2.Will the abandon option value of ancillary business of BOT be influenced by the principal parts of the project？ 3.Is there a need to consider the performance security deposit of ancillary business of BOT？ 4.Will the decision of BOT impact the abandon option value of ancillary business or not？ The thesis will use the Monte Carol Simulation & Finite Difference Method to calculate the abandon option value of ancillary business of Taiwan North-South High-Speed Railway Project (THR), and create the relation between the BOT & it’s ancillary business. The thesis will use the ANOVA & Tuley’s Multiple Comparison Method to validate the relationship, and hope it will let the participator to consider in the future.

Neste trabalho são apresentados os resultados do desenvolvimento e teste de esquemas upwind de alta resolução para o controle da difusão numérica em leis de conservação gerais e problemas em dinâmica dos fluidos. Em particular, são derivados dois novos esquemas: o ALUS (Adaptive Linear Upwind Scheme) e o TOPUS (Third-Order Polynomial Upwind Scheme). Esses esquemas são testados no transporte de escalares, em equações 1D tipo convecção-difusão, em sistemas hiperbólicos 1D, nas equações de Euler 2D da dinâmica dos gases e nas equações de Navier-Stokes incompressíveis 2D/3D. Os esquemas são então associados a uma modelagem algébrica não linear para a simulação de problemas de escoamentos incompressíveis turbulentos 2D com/sem superfícies livres / In this work, results of the development and testing of high-resolution upwind schemes for controlling of the numerical diffusion for general conservation laws and fluid dynamics problems are presented. In particular, two new high-resolution upwind schemes are derived, namely, the ALUS (Adaptive Linear Upwind Scheme) and the TOPUS (Third-Order Polynomial Upwind Scheme). These schemes are tested in scalar transport, 1D convection-diffusion equations, 1D hyperbolic systems, 2D Euler equations of the gas dynamics, and in 2D/3D incompressible Navier-Stokes equations. The schemes are then combined with a nonlinear Reynolds stress algebraic equation model for the simulation of 2D incompressible turbulent flows with/without free surfaces

Apesar de as EDPS que modelam leis de conservação e problemas em dinâmica dos fluídos serem bem estabelecidas, suas soluções numéricas continuam ainda desafiadoras. Em particular, há dois desafios associados à computação e ao entendimento desses problemas: um deles é a formação de descontinuidades (choques) e o outro é o fenômeno turbulência. Ambos os desafios podem ser atribuídos ao tratamento dos termos advectivos não lineares nessas equações de transporte. Dentro deste canário, esta tese apresenta o estudo do desenvolvimento de um novo esquema \"upwind\" de alta resolução e sua associação com modelagem da turbulência. O desempenho do esquema é investigado nas soluções da equação de advecção 1D com dados iniciais descontínuos e de problemas de Riemann 1D para as equações de Burgers, Euler e águas rasas. Além disso, são apresentados resultados numéricos de escoamentos incompressíveis 2D e 3D no regime laminar a altos números de Reynolds. O novo esquema é então associado à modelagem \'capa\' - \'epsilon\' da turbulência para a simulação numérica de escoamentos incompressíveis turbulentos 2D e 3D com superfícies livres móveis. Aplicação, verificação e validação dos métodos numéricos são também fornecidas / Althought the PDEs that model conservation laws and fluid dynamics problems are well established, their numerical solutions have presented a continuing challenge. In particular, there are two challenges associated with the computation and the understanding of these problems, namely, formation of shocks and turbulence. Both challenges can be attributed to the nonlinear advection terms of these transport equations. In this scenario, this thesis presents the study of the development of a new high-resolution upwind scheme and its association with turbulence modelling. The performance of the scheme is investigated by solving the 1D advection equation with discontinuous initial data 1D Riemann problems for Burgers, Euler and shallow water equations. Besides, numerical results for 2D and 3D incompressible laminar flows at high Reynolds number are presented. The new scheme is then associated with the \'capa - \' epsilon\' turbulence model for the simulation of 2D and 3D incompressible turbulent flows with moving free surfaces. Application, verification and validation of the numerical methods are also provided

In der vorliegenden Arbeit untersuchen wir schwache Lösungen, die zu einem geeigneten Sobolevraum gehören, q-elliptischer und parabolischer Systeme partieller Differentialgleichungen auf deren Regularität für den Fall 1 / In the present work we study the regularity of weak solution to q-elliptic and parabolic systems partial differential equations in appropriate Sobolev spaces in case 1

Apesar de as EDPS que modelam leis de conservação e problemas em dinâmica dos fluídos serem bem estabelecidas, suas soluções numéricas continuam ainda desafiadoras. Em particular, há dois desafios associados à computação e ao entendimento desses problemas: um deles é a formação de descontinuidades (choques) e o outro é o fenômeno turbulência. Ambos os desafios podem ser atribuídos ao tratamento dos termos advectivos não lineares nessas equações de transporte. Dentro deste canário, esta tese apresenta o estudo do desenvolvimento de um novo esquema \"upwind\" de alta resolução e sua associação com modelagem da turbulência. O desempenho do esquema é investigado nas soluções da equação de advecção 1D com dados iniciais descontínuos e de problemas de Riemann 1D para as equações de Burgers, Euler e águas rasas. Além disso, são apresentados resultados numéricos de escoamentos incompressíveis 2D e 3D no regime laminar a altos números de Reynolds. O novo esquema é então associado à modelagem \'capa\' - \'epsilon\' da turbulência para a simulação numérica de escoamentos incompressíveis turbulentos 2D e 3D com superfícies livres móveis. Aplicação, verificação e validação dos métodos numéricos são também fornecidas / Althought the PDEs that model conservation laws and fluid dynamics problems are well established, their numerical solutions have presented a continuing challenge. In particular, there are two challenges associated with the computation and the understanding of these problems, namely, formation of shocks and turbulence. Both challenges can be attributed to the nonlinear advection terms of these transport equations. In this scenario, this thesis presents the study of the development of a new high-resolution upwind scheme and its association with turbulence modelling. The performance of the scheme is investigated by solving the 1D advection equation with discontinuous initial data 1D Riemann problems for Burgers, Euler and shallow water equations. Besides, numerical results for 2D and 3D incompressible laminar flows at high Reynolds number are presented. The new scheme is then associated with the \'capa - \' epsilon\' turbulence model for the simulation of 2D and 3D incompressible turbulent flows with moving free surfaces. Application, verification and validation of the numerical methods are also provided

Esse trabalho teve como objetivo contribuir para o debate sobre a importância das políticas de incentivo à inovação no Brasil. Os resultados esperados do uso que as empresas fizeram dos diferentes tipos de instrumentos sobre os gastos em pesquisa e desenvolvimento (P&D) foram avaliados pelo método de diferenças em diferenças. O método permitiu obter as diferenças de gastos entre empresas beneficiárias de instrumentos e as não-beneficiárias em três períodos consecutivos: 2005 em relação à 2003; 2008 em relação à 2005 e de 2011 em relação à 2008. Ao fazer isso, foi possível identificar se tais diferenças foram positivas e significativas, podendo ser atribuídas às influências dos instrumentos. Os instrumentos utilizados foram: incentivos fiscais, Lei de Informática, financiamentos em parcerias, financiamentos sem parcerias e subvenção. E a utilização dos mesmos pelas empresas teve maior relevância no âmbito de diversos programas de apoio à inovação vigentes no país a partir da retomada das políticas industriais e tecnológicas, nos anos 2000. O estudo concluiu que os efeitos positivos e significativos são limitados à determinados grupos tecnológicos e à poucos instrumentos, em geral, de caráter fiscal. Além disso, esses efeitos positivos surgem em apenas um período, sendo que para cada grupo tecnológico foram efetuadas estimativas para três períodos. Também não houve evidências de que os instrumentos financeiros exerçam efeitos significativos sobre as decisões de gastos em pesquisa e desenvolvimento, apesar da maior ênfase dada aos mesmos no período estudado. Os resultados sugerem fraca influência dos mecanismos de apoio à P&D no Brasil sobre o aumento dos gastos privados, apesar dos avanços recentes. / This study aimed to contribute to the debate about the importance of encouraging innovation policies in Brazil. Understanding the role played by public support instruments to research and development activities in relation to private business spending has become fundamental to achieving this end. The expected results of the use that companies made of different types of instruments on spending were evaluated by the method of difference in differences. This allows you to compare, over a certain period of time, the differences in expenses between the companies that made use of any type of instrument and the companies that did not. Thus, the method yielded differences in spending between the beneficiary and nonbeneficiary firms of those instruments of three consecutive periods: 2005 compared to 2003; 2008 compared to 2005 and 2011 compared to 2008. In doing so, it was possible to identify whether these differences were positive and significant and can be attributed to the influence of the instruments. The instruments used were: tax incentives, Information Technology Law, financing partnerships, financing and grants. And their use by companies had most relevance within various programs to support innovation in force in the country from the resumption of industry and technology policy in the 2000s. The study concluded that the positive and significant effects are limited to certain technological groups and the few instruments in general tax character. In addition, these positive effects arise in one period, and for each technology group estimates were made for three periods. There was also no evidence that the financial instruments carry significant effects on spending decisions on research and development, despite the greater emphasis given to them during the study period. The results suggest weak influence of mechanisms to support R&D in Brazil on the rise in private spending, despite progress in recent years.

The Black-Scholes model and its assumptions has endured its fair share of criticism. One problematic issue is the model’s assumption that market volatility is constant. The past decade has seen numerous publications addressing this issue by adapting the Black-Scholes model to incorporate stochastic volatility. In this dissertation, American put options are priced under the Heston stochastic volatility model using the Crank- Nicolson finite difference method in combination with the Projected Over-Relaxation method (PSOR). Due to the early exercise facility, the pricing of American put options is a challenging task, even under constant volatility. Therefore the pricing problem under constant volatility is also included in this dissertation. It involves transforming the Black-Scholes partial differential equation into the heat equation and re-writing the pricing problem as a linear complementary problem. This linear complimentary problem is solved using the Crank-Nicolson finite difference method in combination with the Projected Over-Relaxation method (PSOR). The basic principles to develop the methods necessary to price American put options are covered and the necessary numerical methods are derived. Detailed algorithms for both the constant and the stochastic volatility models, of which no real evidence could be found in literature, are also included in this dissertation. / MSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2013

The Black-Scholes model and its assumptions has endured its fair share of criticism. One problematic issue is the model’s assumption that market volatility is constant. The past decade has seen numerous publications addressing this issue by adapting the Black-Scholes model to incorporate stochastic volatility. In this dissertation, American put options are priced under the Heston stochastic volatility model using the Crank- Nicolson finite difference method in combination with the Projected Over-Relaxation method (PSOR). Due to the early exercise facility, the pricing of American put options is a challenging task, even under constant volatility. Therefore the pricing problem under constant volatility is also included in this dissertation. It involves transforming the Black-Scholes partial differential equation into the heat equation and re-writing the pricing problem as a linear complementary problem. This linear complimentary problem is solved using the Crank-Nicolson finite difference method in combination with the Projected Over-Relaxation method (PSOR). The basic principles to develop the methods necessary to price American put options are covered and the necessary numerical methods are derived. Detailed algorithms for both the constant and the stochastic volatility models, of which no real evidence could be found in literature, are also included in this dissertation. / MSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2013

Cette thèse constitue un ensemble de travaux et de réflexions sur la question de la modélisation d’expériences en nano-optique utilisant la méthode des différences finies dans le domaine fréquentiel (FDFD) et la méthode des différences finies dans le domaine temporel (FDTD). D’abord, un code FDFD bidimensionnel, dédié au calcul de modes propres de guides d’ondes optiques, a été mis en œuvre et testé à travers une comparaison avec des résultats publiés. Dans une deuxième grande partie, nous étudions le piégeage optique de petites particules (de taille microscopique) à l’aide d’une antenne à nano-ouverture papillon (BNA) gravée à l’extrémité d’une sonde de microscope optique métallisée. Le confinement de lumière obtenue à la résonance de la nano-antenne permet un piégeage 3-D des nanoparticules de latex. Une étude systématique a été menée pour quantifier la puissance de la lumière incidente nécessaire pour un piégeage stable. Un bon accord entre les résultats expérimentaux et numériques a été obtenu dans le cas d’une BNA opérant dans l’eau à _ = 1064 nm pour le piégeage de particules de latex de 250 nm de rayon. En outre, les résultats numériques pour de plus petites particules sont présentés et montrent qu’une telle configuration est capable de piéger des particules avec des rayons aussi petits que 30 nm. Troisièmement, nous avons étudié le processus de piégeage optique basé sur l’amélioration du confinement, non seulement du champ électrique comme dans le cas de la BNA, mais aussi du magnétique que peut exhiber l’antenne métallique type diabolo (DA). Cette dernière a été récemment proposée car elle présente une résonance avec un fort confinement magnétique. Nous avons amélioré le design afin qu’une double résonance, électrique et magnétique, ait lieu au centre de la nano-antenne. Ce double confinement a ensuite été exploité pour exalter le gradient de champ au voisinage de l’antenne et ainsi aboutir à de meilleures efficacités de piégeage (moindre puissance). De plus, les résultats des simulations montrent que le processus de piégeage dépend fortement des dimensions des particules et que, pour des géométries particulières, un piégeage sans contact peut être réalisé. Cette structure doublement résonnante ouvre la voie à la conception d’une nouvelle génération de nano-pinces optiques à forte efficacit / This thesis is a set of work and reflections on modeling the experiments in nano-optics by using the finite difference method in the frequency domain (FDFD), and in time domain (FDTD). First, a two-dimensional code FDFD, dedicated to the calculation the eigenmodes of optical waveguides, has been implemented and tested through a comparison with results found in the literature. In a second large part, we study the optical trapping of small particles (of microscopic size) by using a bowtie nanoaperture antenna (BNA) engraved at the end of a metal-coated near-field optical microscope tip. The confinement of light obtained at the resonance of the nano-antenna allows 3-D trapping of latex nanoparticles. A systematic study was conducted to quantify the power of incident light necessary for stable trapping. Good agreement between the experimental and numerical results was obtained in the case of a BNA operating in water at _ = 1064 nm for the trapping of latex particles having a radius of 250 nm-radius. In addition, numerical results for smaller particles are presented and show that such configuration is capable of trapping particles with radii reaching 30 nm. Third, we studied the optical trapping process based on improved confinement of the electric field as in the case of the BNA, but also of the magnetic field, by using a metallic diabolo shape antenna (DA). This latter has been recently proposed because it exhibits resonance with a strong magnetic field confinement. We have improved the design in such a way that a double resonance, electric and magnetic, takes place in the center of the nano-antenna. This dual confinement was then used in order to enhance the field gradient in its vicinity and thus obtain better efficiencies of the trapping (less power). In addition, the simulation results show that the trapping process is greatly dependent of the particles size, and also show that, for specificl geometries, a trapping without contact can be achieved. This doubly resonant structure opens the way to the conception of a new generation of optical nano-tweezers with high efficiency.

Les besoins grandissants de prévisions robustes pour des systèmes complexes conduisent à introduire des modèles mathématiques considérant un nombre croissant de paramètres. Au temps s'ajoutent l'espace, l'aléa, les échelles de dynamiques, donnant lieu à des modèles stochastiques multi-échelles avec dépendance spatiale (modèles spatiaux). Cependant, l'explosion du temps de simulation de tels modèles complique leur utilisation. Leur analyse difficile a néanmoins permis, pour les modèles à une échelle, de développer des outils puissants: loi des grands nombres (LGN), théorème central limite (TCL), ..., puis d'en dériver des modèles simplifiés et algorithmes accélérés. Dans le processus de dérivation, des modèles et algorithmes dits hybrides ont vu le jour dans le cas multi-échelle, mais sans analyse rigoureuse préalable, soulevant ainsi la question d'approximation hybride dont la consistance constitue l'une des motivations principales de cette thèse.En 2012, Crudu, Debussche, Muller et Radulescu établissent des critères d'approximation hybride pour des modèles homogènes en espace de réseaux de régulation de gènes. Le but de cette thèse est de compléter leur travail et le généraliser à un cadre spatial.Nous avons développé et simplifié différents modèles, tous des processus de Markov de sauts pures à temps continu. La démarche met en avant, d'une part, des conditions d'approximations déterministes par des solutions d'équations d'évolution (type réaction-advection-diffusion), et, d'autre part, des conditions d'approximations hybrides par des processus stochastiques hybrides. Dans le cadre des réseaux de réactions biochimiques, un TCL est établi. Il correspond à une approximation hybride d'un modèle homogène simplifié à deux échelles de temps (suivant Crudu et al.). Puis, une LGN est obtenue pour un modèle spatial à deux échelles de temps. Ensuite, une approximation hybride est établie pour un modèle spatial à deux échelles de dynamique en temps et en espace. Enfin, des comportements asymptotiques en grandes populations et en temps long sont présentés pour un modèle d'épidémie de choléra, via une LGN suivie d'une borne supérieure pour les sous-ensembles compacts, dans le cadre d'un principe de grande déviation (PGD) correspondant.À l'avenir, il serait intéressant, entre autres, de varier la géométrie spatiale, de généraliser le TCL, de compléter les estimations du PGD, et d'explorer des systèmes complexes issus d'autres domaines. / The growing needs of precise predictions for complex systems lead to introducing stronger mathematical models, taking into account an increasing number of parameters added to time: space, stochasticity, scales of dynamics. Combining these parameters gives rise to spatial --or spatially inhomogeneous-- multiscale stochastic models. However, such models are difficult to study and their simulation is extremely time consuming, making their use not easy. Still, their analysis has allowed one to develop powerful tools for one scale models, among which are the law of large numbers (LLN) and the central limit theorem (CLT), and, afterward, to derive simpler models and accelrated algorithms. In that deduction process, the so-called hybrid models and algorithms have arisen in the multiscale case, but without any prior rigorous analysis. The question of hybrid approximation then shows up, and its consistency is a particularly important motivation of this PhD thesis.In 2012, criteria for hybrid approximations of some homogeneous regulation gene network models were established by Crudu, Debussche, Muller and Radulescu. The aim of this PhD thesis is to complete their work and generalize it afterward to a spatial framework.We have developed and simplified different models. They all are time continuous pure jump Markov processes. The approach points out the conditions allowing on the the one hand deterministic approximations by solutions of evolution equations of type reaction-advection-diffusion, and, on the other hand, hybrid approximations by hybrid stochastic processes. In the field of biochemical reaction networks, we establish a CLT. It corresponds to a hybrid approximation of a simplified homogeneous model (due to Crudu et al.). Then a LLN is obtained for a spatial model with two time scales. Afterward, a hybrid approximation is established, for a two time-space scales spatial model. Finally, the asymptotic behaviour in large population and long time are respectively presented for a model of cholera epidemic, through a LLN followed by the upper bound for compact sets, in the context of a corresponding large deviation principle (LDP).Interesting future works would be, among others, to study other spatial geometries, to generalize the CLT, to complete the LDP estimates, and to study complex systems from other fields.