Other Statistics and Probability Commons^™

Modeling And Simulation Of Value -At -Risk In The Financial Market Area, Xiangyin Zheng

Doctoral Dissertations

Value-at-Risk (VaR) is a statistical approach to measure market risk. It is widely used by banks, securities firms, commodity and energy merchants, and other trading organizations. The main focus of this research is measuring and analyzing market risk by modeling and simulation of Value-at-Risk for portfolios in the financial market area. The objectives are (1) predicting possible future loss for a financial portfolio from VaR measurement, and (2) identifying how the distributions of the risk factors affect the distribution of the portfolio. Results from (1) and (2) provide valuable information for portfolio optimization and risk management.

The model systems chosen …

Fluid Flow In Micro-Channels: A Stochastic Approach, Hilda Marino Black

Doctoral Dissertations

In this study free molecular flow in a micro-channel was modeled using a stochastic approach, namely the Kolmogorov forward equation in three dimensions. Model equations were discretized using Central Difference and Backward Difference methods and solved using the Jacobi method. Parameters were used that reflect the characteristic geometry of experimental work performed at the Louisiana Tech University Institute for Micromanufacturing.

The solution to the model equations provided the probability density function of the distance traveled by a particle in the micro-channel. From this distribution we obtained the distribution of the residence time of a particle in the micro-channel. Knowledge of …

Cramer-Rao Bound And Optimal Amplitude Estimator Of Superimposed Sinusoidal Signals With Unknown Frequencies, Shaohui Jia

Doctoral Dissertations

This dissertation addresses optimally estimating the amplitudes of superimposed sinusoidal signals with unknown frequencies. The Cramer-Rao Bound of estimating the amplitudes in white Gaussian noise is given, and the maximum likelihood estimator of the amplitudes in this case is shown to be asymptotically efficient at high signal to noise ratio but finite sample size. Applying the theoretical results to signal resolutions, it is shown that the optimal resolution of multiple signals using a finite sample is given by the maximum likelihood estimator of the amplitudes of signals.