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Option Pricing and Virtual Asset Model SystemCheng, Tehung 07 July 2005 (has links)
In the literature, many methods are proposed to value American options. However, due to computational difficulty, there are only approximate solution or numerical method to evaluate American options. It is not easy for general investors either to understand nor to apply.
In this thesis, we build up an option pricing and virtual asset model system, which provides a friendly environment for general public to calculate early exercise boundary of an American option. This system modularize the wellhandled pricing models to provide the investors an easy way to value American options without learning difficult financial theories. The system consists two parts: the first one is an option pricing system, the other one is an asset model simulation system. The option pricing system provides various option pricing methods to the users; the virtual asset model system generates virtual asset prices for different underlying models.

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Experimental And Theoretical Studies Towards The Development Of A Direct 3D Diffuse Optical Tomographic Imaging SystemBiswas, Samir Kumar 01 1900 (has links) (PDF)
Diffuse Optical Tomography is a diagnostic imaging modality where optical parameters such as absorption coefficient, scattering coefficient and refractive index distributions are recovered to form the internal tissue metabolic image. Nearinfrared (NIR) light has the potential to be used as a noninvasive means of diagnostic imaging within the human breast. Due to the diffusive nature of light in tissue, computational modelbased methods are required for functional imaging. The main goal is to recover the spatial variation of optical properties which shed light on the different metabolic states of tissue and tissue like media.
This thesis addresses the issue of quantitative recovery of optical properties of tissuemimicking phantom and pork tissue using diffuse optical tomography (DOT). The main contribution of the present work is the development of robust, efficient and fast optical property reconstruction algorithms for a direct 3D DOT imaging system. There are both theoretical and experimental contributions towards the development of an imaging system and procedures to minimize accurate data collection time, overall system automation as well as development of computational algorithms.
In nurturing the idea of imaging using NIR light into a fully developed direct 3D imaging system, challenges from the theoretical and computational aspects have to be met. The recovery of the optical property distribution in the interior of the object from the often noisy boundary measurements on light, is an illposed ( and nonlinear) problem. This is particularly true, when one is interested in a direct 3D image reconstruction instead of the often employed stacking of 2D crosssections obtained from solving a set of 2D DOT problems. In order to render the DOT, a useful diagnostic imaging tool and a robust reconstruction procedure giving accurate and reliable parameter recovery in the scenario, where the number of unknowns far outnumbers the number of independent data sets that can be gathered (for example, the direct 3D recovery mentioned earlier) is essential. Here, the inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a datamodel misfit function.
An interesting development in this direction has been the development of Broyden’ s and adjoint Broyden’ s methods that avoids direct Jacobian computation in each iteration thereby making the full 3D a reality. Conventional model based iterative image reconstruction (MoBIIR) algorithm uses Newton’ s and it’s variant methods, where it required repeated evaluation of whole Jacobian, which consumes bulk time in reconstruction process. The explicit secant and adjoint information based fast 2D/3D image reconstruction algorithms without repeated evaluation of the Jacobian is proposed in diffuse optical tomography, where the computational time has been decreased many folds by updating the Jacobian successively through low rank update.
An alternative route to the iterative solution is attempted by introducing an artificial dynamics in the system and treating the steadystate response of the artificially evolving dynamical system as a solution. The objective is to consider a novel family of pseudodynamical 2D and 3D systems whose numerical integration in time provides an asymptotic solution to the inverse problem at hand. We convert GaussNewton’ s equation for updates into a pseudodynamical (PD) form by explicitly adding a time derivative term. As the pseudotime integration schemes do not need such explicit matrix inversion and depending on the pseudotime step size, provides for a layer of regularization that in turn helps in superior quality of 2D and 3D image reconstruction.
A cost effective frequency domain Matlab based 2D/3D automated imaging system is designed and built. The complete instrumentation (including PCbased control software) has been developed using a single modulated laser source (wavelength 830nm) and a photomultiplier tube (PMT). The source and detector fiber change their positions dynamically allowing us to gather data at multiple source and detector locations. The fiber positions are adjusted on the phantom surface automatically for scanning variable size phantoms. A heterodyning scheme was used for reading out the measurement using a lockinamplifier. The Matlab program carries out sequence of actions such as instrument control, data acquisition, data organization, data calibration and reconstruction of image.
The GaussNewton’ s, Broyden’ s, adjoint Broyden’ s and pseudotime integration algorithms are evaluated using the simulation data as well as data from the experimental DOT system. Validation of the system and the reconstruction algorithms were carried out on a real tissue, a pork tissue with an embedded fat inhomogeneity. The results were found to match the known parameters closely.

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