Derivative pricing, model calibration, and sensitivity analysis are the three main problems in financial modeling. The purpose of this study is to present an algorithm to improve the pricing process, the calibration process, and the sensitivity analysis of the double Heston model, in the sense of accuracy and efficiency. Using the optimized caching technique, our study reduces the pricing computation time by about 15%. Another contribution of this thesis is: a novel application of the Automatic Differentiation (AD) algorithms in order to achieve a more stable, more accurate, and faster sensitivity analysis for the double Heston model (compared to the classical finite difference methods). This thesis also presents a novel hybrid model by combing the heuristic method Differentiation Evolution, and the gradient method Levenberg--Marquardt algorithm. Our new hybrid model significantly accelerates the calibration process.

We describe techniques for fast compression of time series and hierarchical indexing of compressed series based on the assignment of importance levels to the extrema of time series and their derivatives. We formalize the distance functions used in compression and retrieval techniques. We describe retrieval techinques that use the developed compression and indexing techniques for fast retreval of series from a database that match a given pattern.

Abstract not available

<p>Syftet med denna studie är att, utifrån ett matematikdidaktiskt perspektiv, undersöka hur derivata introduceras i gymnasiets kurs Matematik C. Vi har i huvudsak fokuserat på didaktik och kognitiv utveckling. I en genomgång av relevant litteratur har vi tagit del av teorier och resultat från tidigare forskning inom samma område. Litteraturen försöker besvara frågan om hur lärare på bästa sätt kan överbrygga kognitiva hinder och ge elever en djupare förståelse kring de matematiska sammanhangen.</p><p>Vårt material består av kvalitativa intervjuer med lärare från två skolor och ett antal läroböcker. Genomgången av intervjumaterialet har resulterat i fyra teman att använda som grund för hela studien: allmänt lärande, matematiklärande, derivatbegreppet samt visualisering.</p><p>De lärare vi intervjuar vill alla stimulera elevers intresse för mer avancerad matematik. I princip följer alla, både lärare och läromedel, samma ”mall” när de introducerar derivata. Man knyter gärna an till vardagshändelser och begrepp som till exempel hastighet.</p><p>Den litteratur vi använder, har många förslag och synpunkter på vilket sätt matematikundervisning bör bedrivas på denna nivå. I vissa avseenden skiljer sig dessa från hur intervjumaterialet visar att det verkligen går till. Vår förhoppning är att studien ska bidra till att både vi själva och andra får idéer om utveckling av undervisningen.</p>

Syftet med denna studie är att, utifrån ett matematikdidaktiskt perspektiv, undersöka hur derivata introduceras i gymnasiets kurs Matematik C. Vi har i huvudsak fokuserat på didaktik och kognitiv utveckling. I en genomgång av relevant litteratur har vi tagit del av teorier och resultat från tidigare forskning inom samma område. Litteraturen försöker besvara frågan om hur lärare på bästa sätt kan överbrygga kognitiva hinder och ge elever en djupare förståelse kring de matematiska sammanhangen. Vårt material består av kvalitativa intervjuer med lärare från två skolor och ett antal läroböcker. Genomgången av intervjumaterialet har resulterat i fyra teman att använda som grund för hela studien: allmänt lärande, matematiklärande, derivatbegreppet samt visualisering. De lärare vi intervjuar vill alla stimulera elevers intresse för mer avancerad matematik. I princip följer alla, både lärare och läromedel, samma ”mall” när de introducerar derivata. Man knyter gärna an till vardagshändelser och begrepp som till exempel hastighet. Den litteratur vi använder, har många förslag och synpunkter på vilket sätt matematikundervisning bör bedrivas på denna nivå. I vissa avseenden skiljer sig dessa från hur intervjumaterialet visar att det verkligen går till. Vår förhoppning är att studien ska bidra till att både vi själva och andra får idéer om utveckling av undervisningen.

The key features of dynamics of ultraslowing glass forming systems are their universality in diversity. Its origin is recognized as one of the greatest challenges of condensed matter physics and materials engineering in the XXI century. Similar phenomena are observed on approaching the glass transition in low molecular weight supercooled liquids, polymers, colloidal fluids as well as in solids, for instance in orientationally disordered crystals, spin glass-like magnetic, vortex glasses. Pre-vitreous dynamics is also proposed as a general reference for the category of complex liquids/soft matter systems. The upsurge of the primary relaxation time or related dynamical properties is the basic physical phenomena of the still mysterious previtreous behavior. This means a much more pronounced slowing down than the Arrhenius pattern observed far above the glass transition temperature. Portraying this behavior constitutes one of key checkpoints for theoretical models developed to unwind the glass transition puzzle. However, none of the aforementioned features can answer the understanding that governs the increase of relaxation time in liquids upon cooling. In this thesis we focus on the above questions studying the dynamics of some materials for which their molecules can retain a translational order being orientationally disordered between them upon cooling, which are referred to plastic phases or orientationally disordered (OD) crystalline phases. The work presented in this thesis potentially extends the knowledge of dynamics of OD phases and orientationally glasses (OG), a research topic which has gained interest during the last decades. Through this study, especial attention has been devoted to the phenomenological equations accounting to the temperature dependence of the mean relaxation time describing the orientational dynamics .The study was carried out by the use of BDS as well as two complementary experimental techniques. We show distortion-sensitive and derivative-based empirical analysis of the validity of leading equations for portraying the previtreous evolution of primary relaxation time. A new method for studying the dynamics of glass forming systems is introduced and the minimization procedure is validated and discussed. We present the results divided in two topics, the dynamics of the pure compounds and mixed crystals and the derivative analysis through different existing models. In the first topic we focus on the dynamics of the pure compounds and mixed crystals formed between cycloheptanol and cyclooctanol as well as the a-relaxation dynamics of 1-cyano-adamantane and its mixtures with 1-chloro-adamantane. The second topic is divided in two groups of models, linearized and non-linearized models. In the linearized models we show the application of the derivative based, distortion-sensitive analysis to liquid crystals (LC) and OD phases. We also discuss the results concerning to the cases of the olygomeric liquid epoxy resin (EPON828), neopentylalcohol and neopentylglycol mixture, isooctylcyanobiphenyl and propylene carbonate. The possible empirical correlations between one of the linearized models with the universal pattern for the high frequency wing of the loss curve for primary relaxation time for LCs and OD phases is also shown. In the final part we show that the form of the equation recently introduced by Mauro et al. does not allow a similar straightforward linearization procedure. Unlike the previous models, the involved parameters are not correlated with the slope and the intercept of a linear function. In order to solve this problem, we have introduced the concept of the enthalpy space. The evidences of the existence of crossovers as well as quantitative descriptions are discussed. We show also a new procedure for detecting the crossover in a very easy way. A new kind of crossovers which seems to be impossible to be detected by the classical Stickel transformation is presented. / La principal característica de la dinámica de sistemas vítreos viscosos, es su universalidad en la diversidad. Su origen es uno de los mayores desafíos de la física de la materia condensada y de la ingeniería de materiales en el siglo XXI. La fenomenología típica de las fases vítreas se observan cerca de la transición vítrea en líquidos subenfriados de bajo peso molecular, polímeros, fluidos coloidales, así como en los sólidos con fases orientacionalmente desordenadas. La imposibilidad de explicar las causas del gran aumento del tiempo de relajación al enfriar un líquido, constituye uno de los problemas más importantes no resueltos en materia condensada. Con el objetivo de dar respuesta a dicha interrogante, se han propuesto modelos termodinámicos y dinámicos que han resultado inconsistentes. En esta tesis nos centramos en dicha problemática, estudiando la dinámica orientacional de algunos materiales que al ser enfriados pueden conservar un orden traslacional mientras que se conserva el desorden orientacional de las moléculas que los forman. Dichas fases se conocen como fases plásticas u orientacionalmente desordenadas (OD). El trabajo presentado en esta tesis amplía el conocimiento de la dinámica de dichas fases, un tema de investigación cuyo interés ha aumentado durante las últimas décadas. Se ha dedicado una atención especial a las ecuaciones fenomenológicas que describen la dependencia del tiempo de relajación con la temperatura. El estudio se ha llevado a cabo mediante el uso de espectroscopía dieléctrica de banda ancha, así como mediante el uso de técnicas experimentales complementarias. Se ha introducido un nuevo método para el estudio de la dinámica de los sistemas que dan lugar a fases vítreas. El método ha sido validado y discutido. Los resultados de esta tesis se presentan divididos en dos temas, por un lado, la dinámica de compuestos puros y de los cristales mixtos y, por otro, el análisis mediante el método derivativo aplicado a los diferentes modelos físicos existentes. En el primer tema nos centramos en la dinámica de los compuestos puros y los cristales mixtos formados por cicloheptanol y ciclooctanol, así como la dinámica de la relajación alfa en 1-ciano-adamantano y sus mezclas con 1-cloro-adamantano. El segundo tema se divide en dos grupos de modelos, los modelos lineales y no lineales. En los modelos lineales se muestra la aplicación del procedimiento de derivativo en los cristales líquidos (CL) y las fases OD. También se discuten los resultados relativos a los casos de la resina líquida (EPON828), la mezcla neopentil-alcohol y neopentil-glicol, el carbonato de propileno, así como el CL isooctilcianobifenil. Se discute también la existencia de posibles correlaciones empíricas entre uno de los modelos lineales con el patrón universal para la parte de alta frecuencia de la curva de pérdidas dieléctricas de la relajación primaria para las fases CL y OD. En la parte final se muestra que la forma de la ecuación introducida recientemente por Mauro et al. no permite la linearización mediante el método derivativo. A diferencia de los modelos anteriores, los diferentes parámetros no están correlacionados con la pendiente y el origen de coordenadas de una función lineal. Para resolver este problema, hemos introducido el concepto del espacio entálpico. Se analiza también la existencia de cambios de comportamiento dinámicos y se aportan descripciones cuantitativas. Se muestra también un nuevo procedimiento para detectar los cambios dinámicos de una manera fácil, que permite incluso detectar aquéllos que son obviados mediante el método clásico de Stickel.

This dissertation proposes a finite element procedure for evaluating the high order strain derivatives in nonlocal computational mechanics. The superconvergent second derivative recovery methods used are proven to be effective in evaluating the Laplacian of the equivalent strain based on low order (linear) elements. Current nonlocal finite element techniques with linear elements are limited to structured meshes, while the new technique can deal with unstructured meshes with various element types. Other superconvergent patch recovery (SCP) based nonlocal approaches, such as the patch projection techniques only utilize nodal based patches to evaluate the first derivatives of the strain. The SCP technique has not yet been used for recovery of higher order strain derivatives. The proposed technique is capable of evaluating the Laplacian of the equivalent strain and has the potential for even higher order derivative recovery. The same patches can be easily utilized for error estimation and adaptive meshing for nonlocal problems. We employ two super-convergent patch options: the element based patch with all neighbors or only facing neighbors. The nonlocal strain derivatives can be recovered through either a mesh nodal averaging process or directly at the patch element quadrature points after the patch least square fitting problems are solved. Numerical examples for both strain gradient damage mechanics and strain gradient plasticity problems are given. In summary, the new finite element nonlocal computational technique based on the superconvergent second derivative recovery methods is proven to be robust in evaluating the high order strain derivatives with low order element unstructured meshes.

In this paper we examine energy derivatives pricing. The previous studies considered the same source of uncertainty for the spot and the futures prices. We investigate the problem of futures pricing with two independent sources of risk. In general the structure of the oil and gas futures markets is closely related to some stock indices. Therefore, we develop a model for the futures market and compound derivatives with pricing in accordance with the correspondent index. We derive a framework for energy derivatives pricing, compute the price of the European call option on futures and corresponding hedging strategy. We calculate the price of the European call option adjusted for an index level, study the American put option on futures and corresponding hedging strategies.

In many practical problems in applied sciences, the features of most interest cannot be observed directly, but have to be inferred from other, observable quantities. In particular, many important data acquisition devices provide an access to the measurement of the partial derivatives of a feature of interest rather than sensing its values in a direct way. In this case, the feature has to be recovered through integration which is known to be an ill-posed problem in the presence of noises. Moreover, the problem becomes even less trivial to solve when only a portion of a complete set of partial derivatives is available. In this case, the instability of numerical integration is further aggravated by the loss of information which is necessary to perform the reconstruction in a unique way. As formidable as it may seem, however, the above problem does have a solution in the case when the partial derivatives can be sparsely represented in the range of a linear transform. In this case, the derivatives can be recovered from their incomplete measurements using the theory of compressive sampling (aka compressed sensing), followed by reconstruction of the associated feature/object by means of a suitable integration method. It is known, however, that the overall performance of compressive sampling largely depends on the degree of sparsity of the signal representation, on the one hand, and on the degree of incompleteness of data, on the other hand. Moreover, the general rule is the sparser the signal representation is, the fewer measurements are needed to obtain a useful approximation of the true signal. Thus, one of the most important questions to be addressed in such a case would be of how much incomplete the data is allowed to be for the signal reconstruction to remain useful, and what additional constraints/information could be incorporated into the estimation process to improve the quality of reconstruction in the case of extremely under-sampled data. With these questions in mind, the present proposal introduces a way to augment the standard constraints of compressive sampling by additional information related to some natural properties of the signal to be recovered. In particular, in the case when the latter is defined to be the partial derivatives of a multidimensional signal (e.g. image), such additional information can be derived from some standard properties of the gradient operator. Consequently, the resulting scheme of derivative compressive sampling (DCS) is capable of reliably recovering the signals of interest from much fewer data samples as compared to the case of the standard CS. The signal recovery by means of DCS can be used to improve the performance of many important applications which include stereo imaging, interferometry, coherent optical tomography, and many others. In this proposal, we focus mainly on the application of DCS to the problem of phase unwrapping, whose solution is central to all the aforementioned applications. Specifically, it is shown both conceptually and experimentally that the DCS-based phase unwrapping outperforms a number of alternative approaches in terms of estimation accuracy. Finally, the proposal lists a number of research questions which need to be answered in order to attach strong theoretical guarantees to the practical success of DCS.

In this work, a highly linear broadband Low Noise Amplifier (LNA) is presented. The linearity issue in broadband Radio Frequency (RF) front-end is introduced, followed by an analysis of the specifications and requirements of a broadband LNA through consideration of broadband, multi-standard front-end design. Metal-Oxide- Semiconductor Field-Effect Transistor (MOSFET) non-linearity characteristics cause linearity problems in the RF front-end system. To solve this problem, feedback and the Derivative Superposition Method linearized MOSFET. In this work, novel linearization approaches such as the constant current biasing and the Derivative Superposition Method using a triode region transistor improve linearization stability against Process, Supply Voltage, and Temperature (PVT) variations and increase high power input capability. After analyzing and designing a resistive feedback LNA, novel linearization methods were applied. A highly linear broadband LNA is designed and simulated in 65nm CMOS technology. Simulation results including PVT variation and the Monte Carlo simulation are presented. We obtained -10dB S11, 9.77dB S21, and 4.63dB Noise Figure with IIP3 of 19.18dBm for the designed LNA.