Properties of aggregates are affected by their morphological characteristics, including shape factors, angularity and texture. These morphological characteristics influence the aggregate's mutual interactions and strengths of bonds between the aggregates and the binder. The interactions between aggregates and bond strengths between the aggregate and the binder are vital to rheological properties, related to workability and friction resistance of mixtures. As a consequence, quantification of the aggregate's morphological characteristics is essential for better quality control and performance improvement of aggregates. With advancement of hardware and software, the computation capability has reached the stage to rapidly quantify morphological characteristics at multiple scales using digital imaging techniques. Various computational algorithms have been developed, including Hough transform, Fourier transform, and wavelet analysis, etc. Among the aforementioned computational algorithms, Fourier transform has been implemented in various areas by representing the original image/signal in the spatial domain as a summation of representing functions of varying magnitudes, frequencies and phases in the frequency domain. This dissertation is dedicated to developing the two-dimensional Fourier transform (FFT2) method using the Fourier Transform Interferometry (FTI) system that is capable to quantify aggregate morphological characteristics at different scales. In this dissertation, FFT2 method is adopted to quantify angularity and texture of aggregates based on surface coordinates acquired from digital images in the FTI system. This is followed by a comprehensive review on prevalent aggregate imaging techniques for the quantification of aggregate morphological characteristics, including the second generation of Aggregate Image Measurement System (AIMS II), University of Illinois Aggregate Image Analyzer (UIAIA), the FTI system, etc. Recommendations are made on the usage of aggregate imaging system in the measurements of morphological parameters that are interested. After that, the influence of parent rock, crushing, and abrasion/polishing on aggregate morphological characteristics are evaluated. Atomic-scale roughness is calculated for crystal structures of five representative minerals in four types of minerals (i.e., α-quartz for quartzite/granite/gravel/aplite, dolomite for dolomite, calcite for limestone, haematite and magnetite for iron ore); roughness ranking at atomic-scale is further compared with surface texture ranking at macroscale based on measurement results using the FTI system and AIMS II. Morphological characteristics of aggregates before and after crushing test and micro-deval test are measured to quantitatively evaluate the influences of the crushing process and the abrasion/polishing process on morphological characteristics of aggregates, respectively. / Ph. D.

Conic finance is a brand new quantitative finance theory. The thesis is on the applications of conic finance on South African Financial Markets. Conic finance gives a new perspective on the way people should perceive financial markets. Particularly in incomplete markets, where there are non-unique prices and the residual risk is rampant, conic finance plays a crucial role in providing prices that are acceptable at a stress level. The theory assumes that price depends on the direction of trade and there are two prices, one for buying from the market called the ask price and one for selling to the market called the bid price. The bid-ask spread reects the substantial cost of the unhedgeable risk that is present in the market. The hypothesis being considered in this thesis is whether conic finance can reduce the residual risk? Conic finance models bid-ask prices of cashows by applying the theory of acceptability indices to cashows. The theory of acceptability combines elements of arbitrage pricing theory and expected utility theory. Combining the two theories, set of arbitrage opportunities are extended to the set of all opportunities that a wide range of market participants are prepared to accept. The preferences of the market participants are captured by utility functions. The utility functions lead to the concepts of acceptance sets and the associated coherent risk measures. The acceptance sets (market preferences) are modeled using sets of probability measures. The set accepted by all market participants is the intersection of all the sets, which is convex. The size of this set is characterized by an index of acceptabilty. This index of acceptability allows one to speak of cashows acceptable at a level, known as the stress level. The relevant set of probability measures that can value the cashows properly is found through the use of distortion functions. In the first chapter, we introduce the theory of conic finance and build a foundation that leads to the problem and objectives of the thesis. In chapter two, we build on the foundation built in the previous chapter, and we explain in depth the theory of acceptability indices and coherent risk measures. A brief discussion on coherent risk measures is done here since the theory of acceptability indices builds on coherent risk measures. It is also in this chapter, that some new acceptability indices are introduced. In chapter three, focus is shifted to mathematical tools for financial applications. The chapter can be seen as a prerequisite as it bridges the gap from mathematical tools in complete markets to incomplete markets, which is the market that conic finance theory is trying to exploit. As the chapter ends, models used for continuous time modeling and simulations of stochastic processes are presented. In chapter four, the attention is focussed on the numerical methods that are relevant to the thesis. Details on obtaining parameters using the maximum likelihood method and calibrating the parameters to market prices are presented. Next, option pricing by Fourier transform methods is detailed. Finally a discussion on the bid-ask formulas relevant to the thesis is done. Most of the numerical implementations were carried out in Matlab. Chapter five gives an introduction to the world of option trading strategies. Some illustrations are used to try and explain the option trading strategies. Explanations of the possible scenarios at the expiration date for the different option strategies are also included. Chapter six is the appex of the thesis, where results from possible real market scenarios are presented and discussed. Only numerical results were reported on in the thesis. Empirical experiments could not be done due to limitations of availabilty of real market data. The findings from the numerical experiments showed that the spreads from conic finance are reduced. This results in reduced residual risk and reduced low cost of entering into the trading strategies. The thesis ends with formal discussions of the findings in the thesis and some possible directions for further research in chapter seven. / Thesis (MSc (Risk Analysis))--North-West University, Potchefstroom Campus, 2013.

Conic finance is a brand new quantitative finance theory. The thesis is on the applications of conic finance on South African Financial Markets. Conic finance gives a new perspective on the way people should perceive financial markets. Particularly in incomplete markets, where there are non-unique prices and the residual risk is rampant, conic finance plays a crucial role in providing prices that are acceptable at a stress level. The theory assumes that price depends on the direction of trade and there are two prices, one for buying from the market called the ask price and one for selling to the market called the bid price. The bid-ask spread reects the substantial cost of the unhedgeable risk that is present in the market. The hypothesis being considered in this thesis is whether conic finance can reduce the residual risk? Conic finance models bid-ask prices of cashows by applying the theory of acceptability indices to cashows. The theory of acceptability combines elements of arbitrage pricing theory and expected utility theory. Combining the two theories, set of arbitrage opportunities are extended to the set of all opportunities that a wide range of market participants are prepared to accept. The preferences of the market participants are captured by utility functions. The utility functions lead to the concepts of acceptance sets and the associated coherent risk measures. The acceptance sets (market preferences) are modeled using sets of probability measures. The set accepted by all market participants is the intersection of all the sets, which is convex. The size of this set is characterized by an index of acceptabilty. This index of acceptability allows one to speak of cashows acceptable at a level, known as the stress level. The relevant set of probability measures that can value the cashows properly is found through the use of distortion functions. In the first chapter, we introduce the theory of conic finance and build a foundation that leads to the problem and objectives of the thesis. In chapter two, we build on the foundation built in the previous chapter, and we explain in depth the theory of acceptability indices and coherent risk measures. A brief discussion on coherent risk measures is done here since the theory of acceptability indices builds on coherent risk measures. It is also in this chapter, that some new acceptability indices are introduced. In chapter three, focus is shifted to mathematical tools for financial applications. The chapter can be seen as a prerequisite as it bridges the gap from mathematical tools in complete markets to incomplete markets, which is the market that conic finance theory is trying to exploit. As the chapter ends, models used for continuous time modeling and simulations of stochastic processes are presented. In chapter four, the attention is focussed on the numerical methods that are relevant to the thesis. Details on obtaining parameters using the maximum likelihood method and calibrating the parameters to market prices are presented. Next, option pricing by Fourier transform methods is detailed. Finally a discussion on the bid-ask formulas relevant to the thesis is done. Most of the numerical implementations were carried out in Matlab. Chapter five gives an introduction to the world of option trading strategies. Some illustrations are used to try and explain the option trading strategies. Explanations of the possible scenarios at the expiration date for the different option strategies are also included. Chapter six is the appex of the thesis, where results from possible real market scenarios are presented and discussed. Only numerical results were reported on in the thesis. Empirical experiments could not be done due to limitations of availabilty of real market data. The findings from the numerical experiments showed that the spreads from conic finance are reduced. This results in reduced residual risk and reduced low cost of entering into the trading strategies. The thesis ends with formal discussions of the findings in the thesis and some possible directions for further research in chapter seven. / Thesis (MSc (Risk Analysis))--North-West University, Potchefstroom Campus, 2013.