A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2014. / This dissertation considers the pricing of European and American options. European option prices are determined by the market and can be veri ed by a closed-form solution to the Black-Scholes model. These options can only be exercised at the maturity date. American option prices are not derived from the market and cannot be priced using the same closed-form solution as in the case of the European options because American options can be exercised at any time on or before the maturity date. An initial method was investigated in pricing a European option but could not price American options. Improvements were made producing two robust option pricing models. The results of which were compared to the closed-form solution in the case of European options and a numerical approximation solution in the case of American options. The improved models showed two signi cant bene ts. The rst bene t is the ability to price both European and American options and the second is the ability to calibrate the models to market prices using market data. Changes to the parameters of the models showed the limitations of each improved model. In conclusion, the improved methods are e ective procedures for solving the European and American option pricing problem. Keywords: European options, American options, Markov Decision Processes, Kernel-Based Reinforcement Learning, Calibration.

by Sai-kee Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 74-77). / Acknowledgments --- p.ii / List Of Figures --- p.v / List Of Tables --- p.vii / Abstract --- p.viii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Objective of the Study --- p.2 / Chapter 1.3 --- Our Approach --- p.3 / Chapter 1.4 --- Original Contributions --- p.4 / Chapter 1.5 --- Organization of this Dissertation --- p.5 / Chapter 2 --- Previous Work --- p.6 / Chapter 2.1 --- Absolution orientation approach --- p.6 / Chapter 2.2 --- Relative orientation approach --- p.7 / Chapter 3 --- Calibration using OTV correspondences --- p.12 / Chapter 3.1 --- Problem Statement --- p.12 / Chapter 3.2 --- Recovering the orientation of an OTV from a single view --- p.14 / Chapter 3.3 --- Recovering the transformation parameters between two views --- p.18 / Chapter 3.3.1 --- Recovering R --- p.19 / Chapter 3.3.2 --- Recovering t --- p.20 / Chapter 3.3.3 --- Summary of all the steps --- p.20 / Chapter 3.3.4 --- Recovering R and t using more than 2 OTVs --- p.21 / Chapter 4 --- Experimental Results --- p.23 / Chapter 4.1 --- Simulated Data Experiments --- p.23 / Chapter 4.1.1 --- Error versus the smallest angle among the projected branches of an OTV --- p.23 / Chapter 4.1.2 --- Comparison with a point correspondence algorithm --- p.24 / Chapter 4.2 --- Real Image Experiment --- p.41 / Chapter 5 --- Error Analysis --- p.52 / Chapter 5.1 --- Translation in x only --- p.55 / Chapter 5.1.1 --- Jacobian Matrix on Rotation --- p.56 / Chapter 5.1.2 --- Jacobian Matrix on Translation --- p.57 / Chapter 5.2 --- "Rotation + translation in x, y, z" --- p.60 / Chapter 5.2.1 --- Jacobian Matrix on Rotation --- p.60 / Chapter 5.2.2 --- Jacobian Matrix on Translation --- p.61 / Chapter 5.3 --- "Rotation + translation in x,y" --- p.64 / Chapter 5.3.1 --- Jacobian Matrix on Rotation --- p.65 / Chapter 5.3.2 --- Jacobian Matrix on Translation --- p.65 / Chapter 6 --- Conclusion and Future work --- p.68 / Chapter Appendix A --- Least-squares Approximation of a set of Rotation Matrices --- p.70 / Chapter Appendix B --- Epipolar Lines independent of the Translation Magnitude --- p.72

As the use of digital systems continues to grow, there is an increasing need to convert analog information into the digital domain. Successive Approximation Register (SAR) analog-to-digital converters are used extensively in this regard due to their high resolution, small die area, and moderate conversion speeds. However, capacitor mismatch within the SAR converter is a limiting factor in its accuracy and resolution. Without some form of calibration, a SAR converter can only reasonably achieve an accuracy of 10 bits. The Split-ADC technique is a digital, deterministic, background self-calibration algorithm that can be applied to the SAR converter. This thesis describes the circuit design and physical implementation of a novel 16-bit 1MS/s SAR analog-to-digital converter for use with the Split-ADC calibration algorithm. The system was designed using the Jazz 0.18um CMOS process, successfully operates at 1MS/s, and consumes a die area of 1.2mm2. The calibration algorithm was applied, showing an improvement in the overall accuracy of the converter.

The need for custom footwear among the consumers is growing every day. Serious research is being undertaken with regards to the fit and comfort of the footwear. The integration of scanning systems in the footwear and orthotic industries have played a significant role in generating 3D digital representation of the foot for automated measurements from which a custom footwear or an orthosis is manufactured. The cost of such systems is considerably high for many manufacturers due to their expensive components, complex processing algorithms and difficult calibration techniques. This thesis presents a fast and robust calibration technique for a low-cost 3D laser scanner. The calibration technique is based on determining the mathematical relationship that relates the image coordinates to the real world coordinates. The relationship is determined by mapping the known real world coordinates of a reference object to its corresponding image coordinates by multivariate polynomial regression. With the developed mathematical relationship, 3D data points can be obtained from the 2D images of any object placed in the scanner. An image processing script is developed to detect the 2D image points of the laser profile in a series of scan images from 8 cameras. The detected 2D image points are reconstructed into 3D data points based on the mathematical model developed by the calibration process. Following that, the output model is achieved by triangulating the 3D data points as a mesh model with vertices and normals. The data is exported as a computer aided design (CAD) software readable format for viewing and measuring. This method proves to be less complex and the scanner was able to generate 3D models with an accuracy of +/-0.05 cm. The 3D data points from the output model were compared against a reference model scanned by an industrial grade scanner to verify and validate the result. The devised methodology for calibrating the 3D laser scanner can be employed to obtain accurate and reliable 3D data of the foot shape and it has been successfully tested with several participants.

第23回名古屋大学年代測定総合研究センターシンポジウム平成22(2010)年度報告

This thesis presented a complete measurement method for accurate characterization of balanced devices using two-port vector network analyzer. Combining renormalization and mixed-mode transformation techniques, this method is good for coaxial components. At first, the feasibility of the method was confirmed with the help of ADS simulation. Then a real example of Marchand balun fabricated on FR4 substrate was measured with calibrated mixed-mode S-parameters that have been further verified by full-wave simulations. The measurement system developed based on this method does not require any additional hardware to the vector network analyzer. This system can be also applied to the measurement of on-wafer components with the help of some microwave switches.

Section to section alignment is a preliminary step to the creation of three dimensional reconstructions from serial section electron micrographs. Typically, the micrograph of one section is aligned to its neighbors by analyzing a set of fiducial points to calculate an appropriate polynomial transform. This transform is then used to map all of the pixels of the micrograph into alignment. Such transforms are usually linear or piecewise linear in order to limit the accumulation of small errors, which may occur with the use of higher–order approximations. Linear alignment is unable to correct common higher order geometric distortions, such as lens distortion in the case of TEM, and scan distortion in the case of transmission-mode SEM. Here, we attempt to show that standard calibration replicas may be used to calculate a high order distortion model despite the irregularities that are often present in them. We show that SEM scan distortion has much less of an effect than TEM lens distortion; however, the effect of TEM distortion on prior geometric measurements made over three-dimensional reconstructions of dendrites, axons, and synapses and their subcellular compartments is negligible. / text

The trend to integrate more and more processing cores and memory cores into a single module has increased the overall size of chips to the point where global interconnects between sub-units are becoming harder and harder to route and meet timing rules and requirements. The traditional way of routing interconnects and the use of uniform, unidirectional, point to point busses may no longer be optimal for certain designs where metal layers and chip area for interconnects are limited. The need for a more flexible routing methodology is necessary and can be achieved by using routing and calibration techniques currently being implemented at board level design. This report proposes the use of non-uniform, bidirectional, and possibly multi-point loads global interconnects within a single chip module through the use of on chip calibration techniques to compensate for less restrictive wiring rules for certain chip designs. This report will also apply a widely used digital calibration technique to simulate the implementation on a field programmable gate array. / text

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Reliable predictions of reservoir flow response corresponding to various recovery schemes require a realistic geological model of heterogeneity and an understanding of its relationship with the flow properties. This dissertation presents results on the implementation of a novel approach for the integration of dynamic data into reservoir models that combines stochastic techniques for simultaneous calibration of geological models and multiphase flow functions associated with porelevel spatial representations of porous media. In this probabilistic approach, a stochastic simulator is used to model the spatial distribution of a discrete number of rock types identified by rock/connectivity indexes (CIs). Each CI corresponds to a particular pore network structure with a characteristic connectivity. Primary drainage and imbibition displacement processes are modeled on the 3-D pore networks to generate multiphase flow functions corresponding to networks with different CIs. During history matching, the stochastic simulator perturbs the spatial distribution of the CIs to match the simulated pressures and flow rates to historic data, while preserving the geological model of heterogeneity. This goal is accomplished by applying a probabilistic approach for gradual deformation of spatial distribution of rock types characterized by different CIs. Perturbation of the CIs in turn results in the update of all the flow functions including the effective permeability, porosity of the rock, the relative permeabilities and capillary pressure. The convergence rate of the proposed method is comparable to other current techniques with the distinction of enabling consistent updates to all the flow functions. The resultant models are geologically consistent in terms of all the flow functions, and consequently, predictions obtained using these models are likely to be more accurate. To compare and contrast this comprehensive approach to reservoir modeling against other approaches that rely on modeling and perturbing only the permeability field, a realistic case study is presented with implementation of both approaches. Comparison is made with the history-matched model obtained only by perturbing permeability. It is argued that reliable predictions of future production can only be made when the entire suite of flow functions is consistent with the real reservoir.