Mak Nga-sze. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 45-46). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Purpose --- p.2 / Chapter 1.2 --- Flow of the study --- p.3 / Chapter 2 --- Review of Equity Linked Securities --- p.5 / Chapter 2.1 --- Backgrond of Equity Linked Securities in Hong Kong --- p.5 / Chapter 2.2 --- Differences of trading between listed and non-listed ELIs --- p.7 / Chapter 2.3 --- Non-listed ELIs --- p.9 / Chapter 2.3.1 --- Definition --- p.9 / Chapter 2.3.2 --- Variables specification --- p.11 / Chapter 2.3.3 --- Payoff possibilities --- p.13 / Chapter 3 --- Data --- p.17 / Chapter 3.1 --- Data sources --- p.17 / Chapter 3.2 --- Data treatment --- p.18 / Chapter 4 --- Methodology --- p.21 / Chapter 4.1 --- Volatility --- p.23 / Chapter 4.2 --- Implied volatility by CRR binomial Tree --- p.24 / Chapter 4.3 --- Historical volatility --- p.26 / Chapter 5 --- Estimation of Empirical Data --- p.28 / Chapter 5.1 --- Statistical results of the issuer's profit margin --- p.29 / Chapter 5.2 --- Empirical analysis of the profit margin trends --- p.31 / Chapter 5.2.1 --- Factor 1: Volatility --- p.34 / Chapter 5.2.2 --- Factor 2: Trading volume --- p.34 / Chapter 6 --- Conclusion --- p.37 / Chapter 6.1 --- Conclusion --- p.37 / Chapter 6.2 --- Extensions --- p.38 / Appendix --- p.40 / Chapter .1 --- "Tables of non-listed ELIs in Hong Kong, updated to January 31,2005" --- p.40 / Chapter .2 --- "Stock options in HKEx, lastest to June 2004" --- p.43 / Chapter .3 --- Histograms of the issuer's profit margins --- p.44 / References --- p.45

Lau, Kai Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 74-78). / INTRODUCTION --- p.2 / COVERED WARRANTS AND STOCK OPTIONS: A BRIEF BACKGROUND --- p.6 / Chapter a) --- covered warrants --- p.6 / Chapter b) --- Stock Options --- p.10 / Chapter c) --- covered warrants and stock options： a comparison --- p.14 / Chapter d) --- pricing difference between covered warrants and stock options --- p.18 / LITERATURE REVIEW --- p.20 / Chapter a) --- Introduction --- p.20 / Chapter b) --- theory on issuing of stock options --- p.21 / Chapter c) --- the introduction of stock options --- p.26 / Chapter i) --- Stock Options in United States --- p.26 / Chapter ii) --- Stock Options in United Kingdom --- p.28 / Chapter iii) --- Stock Options in Canada --- p.28 / Chapter iv) --- Options in Asia --- p.29 / Chapter d) --- Return Volatility and Trading Volume --- p.31 / Chapter i) --- Introduction --- p.31 / Chapter ii) --- Mixture of Distribution Hypothesis --- p.32 / Chapter iii) --- Classical Model of the Mixture of Distributions Hypothesis --- p.35 / Chapter iv) --- Recent Empirical Model of the Mixture of Distribution Hypothesis --- p.37 / DATA --- p.40 / METHODOLOGY --- p.43 / Chapter a) --- introduction --- p.43 / Chapter b) --- informational efficiency in the cash market --- p.45 / Chapter i) --- Model for Information Arrival and Price Adjustment --- p.46 / Chapter ii) --- Results --- p.48 / Chapter iii) --- An Overall Effect on the Cash market --- p.55 / Chapter c) --- information Cost and Trading Cost in Covered Warrants Market --- p.57 / Chapter i) --- Introduction --- p.57 / Chapter ii) --- Spread function for Covered Warrants --- p.62 / Chapter iii) --- Results --- p.63 / Chapter iv) --- Adjustments for Moneyness --- p.67 / CONCLUSION --- p.70 / REFERENCES --- p.74

The main goal of my diploma work on the topic "Derivative in apllied problems a digest of solved examples" is to create a set of solved exercises that somehow use calculus during solving. The collection contains 43 solved practical problems relating to calculus of one or two variables. This collection intends to serve as a training aid for students of middle or high schools. For a better overview individual tasks are sorted by appropriate fields of science (mathematical, biological, physical, economic).

Orientador: José Mario Martínez Pérez / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T03:18:55Z (GMT). No. of bitstreams: 1 Sobral_FranciscoNogueiraCalmon_D.pdf: 3255516 bytes, checksum: 380cc11e2ad93213e66f456ef5945f1c (MD5) Previous issue date: 2012 / Resumo: Os problemas de otimização sem derivadas surgem de modelos para os quais as derivadas das funções e das restrições envolvidas, por alguma razão, não estão disponíveis. Os motivos variam desde usuários que não querem programar as derivadas até funções excessivamente complexas e caixas-pretas, oriundas de simulações só possíveis graças ao crescimento na capacidade de processamento dos computadores. Acompanhando esse crescimento, o número de algoritmos para resolver problemas de otimização sem derivadas aumentou nos últimos anos. Porém, poucos são aqueles que conseguem lidar de forma eficiente com problemas cujos domínios são magros, como, por exemplo, quando há restrições de igualdade. Neste trabalho, apresentamos a teoria e implementação de dois algoritmos capazes de trabalhar com domínios magros em problemas de otimização sem derivadas. Ambos partem da premissa de que a parte mais custosa na resolução é a avaliação da função objetivo. Com isso em mente, o processo de resolução é dividido em duas fases. Na fase de restauração, buscamos por pontos menos inviáveis sem utilizar avaliações da função objetivo. Na fase de minimização, ou otimização, o objetivo é reduzir a função objetivo com o uso de algoritmos bem estabelecidos para problemas sem derivadas com restrições simples. O primeiro algoritmo utiliza ideias de Restauração Inexata associadas a uma tolerância decrescente à inviabilidade. Utilizando hipóteses simples e usuais dos métodos de busca direta direcional, mostramos propriedades de convergência a minimizadores globais. O segundo algoritmo recupera totalmente os resultados teóricos de um algoritmo recente de Restauração Inexata com busca linear e aplica-se a problemas nos quais apenas as derivadas da função objetivo não estão disponíveis. Testes numéricos mostram as boas propriedades dos dois algoritmos, em particular quando comparados com algoritmos baseados em penalidades / Abstract: Derivative-free optimization problems arise from models whose derivatives of some functions are not available. This information is unavailable due to extremely complex and black-box functions, originated from simulation procedures, or even to user inability. Following the growth in the number of applications, the number of derivative-free algorithms has increased in the last years. However, few algorithms are able to handle thin feasible domains efficiently, for example, in the presence of equality nonlinear constraints. In the present work, we describe the theory and implementation of two algorithms capable of dealing with thin-constrained derivative-free problems. Their definition considers that the objective function evaluation is the most expensive part of the problem. Based on this principle, the process of solving a problem is split into two phases. In the restoration phase, we try to improve the feasibility without evaluating the objective function. In the minimization phase, the aim is to decrease the objective function value by using well-established algorithms in order to solve derivative-free problems with simple constraints. The _rst algorithm uses Inexact Restoration ideas together with a decreasing infeasibility tolerance. Under the usual hypotheses of direct search methods, we show global minimization results. The second algorithm extends to the derivative-free case all the theoretical results obtained in a recent line-search Inexact Restoration algorithm. In this approach, only the derivatives of the objective function are not available. We perform numerical experiments to show the advantages of each algorithm, in particular when comparing with penalty-like algorithms / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Thesis (M.Sc. (Applied Mathematics)) -- University of Limpopo, 2019 / Functional Itˆo calculus is based on an extension of the classical Itˆo calculus to functionals depending on the entire past evolution of the underlying paths and not only on its current value. The calculus builds on F¨ollmer’s deterministic proof of the Itˆo formula Föllmer (1981) and a notion of pathwise functional derivative recently proposed by Dupire (2019). There are no smoothness assumptions required on the functionals, however, they are required to possess certain directional derivatives which may be computed pathwise, see Cont and Fournié (2013); Schied and Voloshchenko (2016a); Cont (2012). In this project we revise the functional Itô calculus together with the notion of quadratic variation. We compute the pathwise change of variable formula utilizing the functional Itô calculus and the quadratic variation notion. We study the martingale representation for the case of weak derivatives, we allow the vertical operator, rX, to operate on continuous functionals on the space of square-integrable Ft-martingales with zero initial value. We approximate the hedging strategy, H, for the case of path-dependent functionals, with Lipschitz continuous coefficients. We study some hedging strategies on the class of discounted market models satisfying the quadratic variation and the non-degeneracy properties. In the classical case of the Black-Scholes, Greeks are an important part of risk-management so we compute Greeks of the price given by path-dependent functionals. Lastly we show that they relate to the classical case in the form of examples. / NRF and AIMS-SA

Many partial differential equations (PDEs) admit conserved quantities like mass or energy. Those quantities are often essential to establish well-posed results. When approximating a PDE by a finite-difference scheme, it is natural to ask whether related discretized quantities remain conserved under the scheme. Such conservation may establish the stability of the numerical scheme. We present an algorithm for checking the preservation of a polynomial quantity under a polynomial finite-difference scheme. In our algorithm, schemes can be explicit or implicit, have higher-order time and space derivatives, and an arbitrary number of variables. Additionally, we present an algorithm for, given a scheme, finding conserved quantities. We illustrate our algorithm by studying several finite-difference schemes.

Abstract in English / In this dissertation we apply linear evolution equations to the Newtonian derivative, Caputo time fractional derivative and $-time fractional derivative. It is notable that the most utilized fractional order derivatives for modelling true life challenges are Riemann- Liouville and Caputo fractional derivatives, however these fractional derivatives have the same weakness of not satisfying the chain rule, which is one of the most important elements of the match asymptotic method [2, 3, 16]. Furthermore the classical bounded perturbation theorem associated with Riemann-Liouville and Caputo fractional derivatives has con rmed not to be in general truthful for these models, particularly for solution operators of evolution systems of a derivative with fractional parameter ' that is less than one (0 < ' < 1) [29]. To solve this problem, we introduce the derivative with new parameter, which is de ned as a local derivative but has a fractional order called $-derivative and apply this derivative to linear evolution equation and to support what we have done in the theory, we utilize application to population dynamics and we provide the numerical simulations for particular cases. / Mathematical Sciences / M.Sc. (Applied Mathematics)

In partial differential equations (PDEs), conserved quantities like mass and momentum are fundamental to understanding the behavior of the described physical systems. The preservation of conserved quantities is essential when using numerical schemes to approximate solutions of corresponding PDEs. If the discrete solutions obtained through these schemes fail to preserve the conserved quantities, they may be physically meaningless and unreliable. Previous approaches focused on checking conservation in PDEs and numerical schemes, but they did not give adequate attention to systematically handling parameters. This is a crucial aspect because many PDEs and numerical schemes have parameters that need to be dealt with systematically. Here, we investigate if the discrete analog of a conserved quantity is preserved under the solution induced by a parametric finite difference method. In this thesis, we modify and enhance a pre-existing algorithm to effectively and reliably deduce conserved quantities in the context of parametric schemes, using the concept of comprehensive Groebner systems. The main contribution of this work is the development of a versatile algorithm capable of handling various parametric explicit and implicit schemes, higher-order derivatives, and multiple spatial dimensions. The algorithm’s effectiveness and efficiency are demonstrated through examples and applications. In particular, we illustrate the process of selecting an appropriate numerical scheme among a family of potential discretization for a given PDE.

In this work, hydrophilic fluorene-based derivatives that contain ethylene oxide substituents, have been synthesized and characterized for potential use as new fluorophores for bioimaging applications and for fluorescence sensing of heavy metals. Symmetrical and unsymmetrical fluorene derivatives based on structural types of acceptor-pi-acceptor, acceptor-pi-donor, and donor-pi-donor were characterized by TGA, UV-vis absorption, fluorescence emission, lifetime, anisotropy, and two-photon absorption (2PA) cross section. They were found to possess high thermal stability, high photostability, high fluorescence quantum yields, and generally large two-photon absorption cross sections, making them quite suitable for new probes in single-photon absorption and two-photon absorption fluorescence microscopy imaging. Novel hydrophilic fluorene derivatives were synthesized from fluorene in multiple steps employing the metal-catalyzed Heck coupling reaction, the Stille reaction, the Sonogashira reaction, the Ullmann condensation reaction, and "click" chemistry. To increase the hydrophilicity of the new compounds, ethylene oxide substituents were utilized for to impart water solubility. An alternative alkylation methodology using ethyleneoxy tosylates was introduced for the synthesis of ethylene oxide-containing fluorene derivatives. Several of these hydrophilic derivatives were incubated into various cell lines as new probes for both conventional and two-photon absorption fluorescence bioimaging. These compounds were biocompatible, exhibiting low cytotoxicity as determined by cell viability studies, and displayed colocalization for selected cellular organelles. In addition, hydrophilic bis(1,2,3-triazolyl)fluorene derivatives were found to exhibit sensitive fluorescence responses in the presence of certain heavy metal, and were selective for sensing zinc and mercury over other a number of other metal ions relevant to living cells or other biological environments. The UV-vis absorption and fluorescence emission spectra of the complexes exhibited a blue-shifted absorption and emission for selective metal chelation upon binding to zinc and mercury(II) ions, resulting in an approximately two-fold enhanced fluorescence response. Fluorescence titration studies revealed that the complexes of 1:2 and 1:3 ligand to metal formed with binding constant values of 108 and 1014 for zinc and mercury ions, respectively. Finally, preliminary experiments were performed to explore the possibility of employing select hydrophilic fluorene-based derivatives in the synthesis of hydrophilic fluorescent gold nanoparticles. Although results are very preliminary, the aim is to use such materials for other biomedical applications, such as surface enhanced scattering resonance and noninvasive photothermal therapy to diagnose and to treat cancers. Thus, this research had led to the discovery of alternative methodologies for synthesis of hydrophilic fluorene derivatives by alkylation with alkyl tosylates and synthesis of hydrophilic fluorescent molecule capped gold nanoparticles. Furthermore, several novel hydrophilic fluorene-based derivatives were synthesized and characterized for their linear and nonlinear photophysical properties, and are now available for further examination of their bioimaging and sensing applications.

La dérivée est un concept important dans les cours de calcul. Dans certains pays comme au Canada et en France, il est enseigné au niveau collégial tandis qu’en Afrique et en particulier au Cameroun, on l’enseigne au niveau secondaire car la dérivée intervient dans l’étude des variations d’une fonction. Cette thèse dont le titre est : Analyse praxéologique des pratiques des enseignants et de leur utilisation de ressources pour l’enseignement de la dérivée. Une étude de cas dans l’enseignement secondaire général au Cameroun part du constat selon lequel de nombreux élèves et étudiants rencontrent des difficultés avec la notion de dérivée et que ces difficultés s’observent dans leurs résultats scolaires et académiques. Au vu de l’importance de la dérivée pour les différents parcours universitaires en sciences, nous nous intéressons aux pratiques des enseignants de mathématiques et notamment leurs praxéologies didactiques autour de la dérivée mais aussi, nous voulons comprendre les raisons qui justifient les choix faits par ces enseignants. La recherche essaie de répondre à la question de savoir quelles sont les pratiques des enseignants et les ressources utilisées par ces derniers pour l’enseignement de la dérivée? La recherche se propose ainsi d’identifier les praxéologies que les enseignants développent dans leur utilisation des ressources pour préparer leurs leçons et pour enseigner la dérivée. Nous ne nous limitons pas aux praxéologies observables mais nous aimerons comprendre les raisons qui justifient les choix opérés par ces enseignants et les contraintes institutionnelles auxquelles ils font face. Deux cadres théoriques encadrent cette recherche : la Théorie Anthropologique de la Didactique (TAD) qui nous permet d’analyser les types de tâches, les techniques, les technologies et les théories justifiant les technologies employées dans les ressources des enseignants et dans leurs pratiques enseignantes. De même, nous utilisons l’Approche Documentaire du Didactique (ADD) afin d’analyser les ressources institutionnelles et les autres ressources que les enseignants utilisent pour enseigner la dérivée. Pour analyser l’utilisation des ressources des enseignants, nous mettons un accent sur les objectifs et les sous-objectifs visés, les règles d’action, les invariants opératoires et les inférences éventuelles. Sur le plan méthodologique, nous utilisons une étude de cas impliquant trois enseignants qui enseignent la dérivée aux élèves de première. Nous utilisons des entretiens semi-dirigés afin d’analyser les choix que font les enseignants lors de la préparation des cours mais et surtout les raisons qui justifient ces choix; les observations vidéo-filmées permettent de savoir comment les enseignants introduisent la dérivée en un point et sur un intervalle et l’analyse des documents tels que les programmes de mathématiques, les manuels scolaires et d’autres ressources des enseignants employés dans la préparation des cours. Le principal résultat de cette thèse est l’identification du poids des ressources institutionnelles et de l’examen de fin d’année sur les praxéologies mathématiques et sur la manière dont les enseignants utilisent ces ressources. Nous discutons de ce résultat en tenant compte du rapport personnel des enseignants et des praxéologies développées dans les manuels et lors de l’enseignement. / Derivatives are one of the most important topics studied in high school (in many countries) and postsecondary mathematics. Many students must learn this topic to pursue their university studies and as a gateway to learn other mathematical topics in various other fields. In Cameroon, secondary teaching lasts from 12 to 18 years old. In this context, what in other countries is considered as pre-university courses, or college, in Cameroon is still called secondary. Derivatives are introduced in the last but one year of this cycle, called première (students are 17), after the topics of function, limit, and continuity. In this thesis, we examined teachers’ practices and their use of resources while teaching derivatives. This study in general secondary education in Cameroon starts from the observation that many pupils and students encounter difficulties with the notion of derivative and that these difficulties are observed in their academic results. The research attempts to identify the tasks, techniques and technologies developed in the resources used by these teachers. It also tries to describe the patterns of use of resources by closely observing the objectives pursued, the rules of action and the operational invariants put in place when using resources. We do not limit ourselves to describing the practices of teachers, but we would like to understand the reasons that justify their choices and the institutional constraints they face. Since we are interested in teachers’ practices and their use of resources to teach derivatives, we use elements of the anthropological theory of the didactic (ATD) to analyze the types of tasks, the techniques, technologies, and theories justifying the technologies used in teachers' resources and teaching practices. By using DA, we understand that teachers, to prepare their teaching, use variety of resources. These resources aiming to teach this content together with the schemes of use of these resources result in a document and these schemes of use of resources is influenced by the teacher’s own personal relationship. The participants in this study were three teachers who teach derivatives to first-class students. We use semi-structured interviews to analyse the choices teachers make when preparing courses, but above all the reasons that justify these choices and video to observe how teachers introduce the derivative. The video shows how teachers introduce the derivative at a point and on an interval. Others analyses helps us understanding how this content is introduced on math programs, textbooks and other teacher resources used in the preparation of courses. The main result of this thesis is the identification of the weight of institutional resources and the end-of-year examination on mathematical praxeology’s and on the way, teachers use these resources. We discuss this result considering the personal relationship of teachers and the praxeology’s developed in textbooks and during teaching.